Pub Date : 2023-12-13DOI: 10.1080/10652469.2023.2291399
Nguyen Minh Khoa
Published in Integral Transforms and Special Functions (Ahead of Print, 2023)
发表于《积分变换与特殊函数》（2023 年提前出版）
{"title":"A response letter for the editor's reports on the paper: On the polyconvolution operator with a trigonometric weight function for Hartley integral transforms and applications","authors":"Nguyen Minh Khoa","doi":"10.1080/10652469.2023.2291399","DOIUrl":"https://doi.org/10.1080/10652469.2023.2291399","url":null,"abstract":"Published in Integral Transforms and Special Functions (Ahead of Print, 2023)","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"267 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138715025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-13DOI: 10.1080/10652469.2023.2291389
Samir Kallel
The inversion of Bessel potentials is given by using a special-type weighted wavelet transform in the context of Dunkl harmonic analysis on IRd. It has also proved the Calderón-type reproducing for...
{"title":"Inversion of Bessel potentials associated with the Dunkl operators on IRd","authors":"Samir Kallel","doi":"10.1080/10652469.2023.2291389","DOIUrl":"https://doi.org/10.1080/10652469.2023.2291389","url":null,"abstract":"The inversion of Bessel potentials is given by using a special-type weighted wavelet transform in the context of Dunkl harmonic analysis on IRd. It has also proved the Calderón-type reproducing for...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"57 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138690328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-13DOI: 10.1080/10652469.2023.2291380
S. S. Volosivets
In this paper, we give necessary and sufficient conditions for a continuous on R+ function f to belong the symmetric generalized Lipschitz classes defined by the Mellin translation in terms of grow...
本文给出了 R+ 上连续函数 f 属于梅林平移定义的对称广义 Lipschitz 类的必要条件和充分条件。
{"title":"Boas-type results for Mellin transform","authors":"S. S. Volosivets","doi":"10.1080/10652469.2023.2291380","DOIUrl":"https://doi.org/10.1080/10652469.2023.2291380","url":null,"abstract":"In this paper, we give necessary and sufficient conditions for a continuous on R+ function f to belong the symmetric generalized Lipschitz classes defined by the Mellin translation in terms of grow...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"2 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138714831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-27DOI: 10.1080/10652469.2023.2287056
Snježana Maksimović
We prove the continuity of the fractional Stockwell transform and the corresponding synthesis operator on the spaces of highly localized functions over R and R×R∖{0}, respectively, and their duals....
{"title":"Fractional Stockwell transform of Lizorkin distributions","authors":"Snježana Maksimović","doi":"10.1080/10652469.2023.2287056","DOIUrl":"https://doi.org/10.1080/10652469.2023.2287056","url":null,"abstract":"We prove the continuity of the fractional Stockwell transform and the corresponding synthesis operator on the spaces of highly localized functions over R and R×R∖{0}, respectively, and their duals....","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"43 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138515272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1080/10652469.2023.2278143
Fethi Bouzeffour, Wissem Jedidi
AbstractIn this paper, we introduce a new type of singular first-order differential-difference operator of Dunkl type on the real line. This operator is obtained as a limiting case from both the first-order Dunkl-type operators corresponding to Bannai-Ito and Big 1-Jacobi orthogonal polynomials. We provide an explicit expression for the eigenfunction of this operator in terms of Bessel functions. The obtained kernel is called the Big Hartley function, which is a generalization of the usual Hartley kernel and the little Hartley function studied in Bouzeffour [The generalized Hartley transform. Integral Transforms Spec Funct. 2014;25(3):230–239]. Additionally, we present a new product formula for the little Hartley function, which is related to the Kingman-Bessel hypergroup and the Rosler-Dunkl signed hypergroup. Finally, we investigate inversion formulae for the transforms of both the little Hartley function and the big Hartley function.Keywords: Generalized differential-difference operatorBessel functionsHartley transform Plancherel formula2010 Mathematics Subject Classifications: 42A3842B1043A3243A15 AcknowledgmentsThe first-named author expresses appreciation for the support provided by Researchers Supporting Project Number (RSPD2023R974), King Saud University, Riyadh, Saudi Arabia.Disclosure statementThe authors declare that she has no conflicts of interest.Data AvailabilityNo data has been used for producing the result of this paper.
{"title":"On the Big Hartley transform","authors":"Fethi Bouzeffour, Wissem Jedidi","doi":"10.1080/10652469.2023.2278143","DOIUrl":"https://doi.org/10.1080/10652469.2023.2278143","url":null,"abstract":"AbstractIn this paper, we introduce a new type of singular first-order differential-difference operator of Dunkl type on the real line. This operator is obtained as a limiting case from both the first-order Dunkl-type operators corresponding to Bannai-Ito and Big 1-Jacobi orthogonal polynomials. We provide an explicit expression for the eigenfunction of this operator in terms of Bessel functions. The obtained kernel is called the Big Hartley function, which is a generalization of the usual Hartley kernel and the little Hartley function studied in Bouzeffour [The generalized Hartley transform. Integral Transforms Spec Funct. 2014;25(3):230–239]. Additionally, we present a new product formula for the little Hartley function, which is related to the Kingman-Bessel hypergroup and the Rosler-Dunkl signed hypergroup. Finally, we investigate inversion formulae for the transforms of both the little Hartley function and the big Hartley function.Keywords: Generalized differential-difference operatorBessel functionsHartley transform Plancherel formula2010 Mathematics Subject Classifications: 42A3842B1043A3243A15 AcknowledgmentsThe first-named author expresses appreciation for the support provided by Researchers Supporting Project Number (RSPD2023R974), King Saud University, Riyadh, Saudi Arabia.Disclosure statementThe authors declare that she has no conflicts of interest.Data AvailabilityNo data has been used for producing the result of this paper.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"55 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1080/10652469.2023.2275129
Selma Negzaoui, Nesrin Yousfi
AbstractIn this paper, we aim to establish an L2 inequality for a Modified Struve transform of order α, denoted as Sα. For this purpose, we use Titchmarsh's method consisting of applying Mellin transform to invert asymmetrical Fourier transforms. We obtain the inversion formula and the L2 estimation of the Modified Struve transform Sα. As an application, we prove the Heisenberg uncertainty principle for Sα.Keywords: L2 inequalityModified Struve transforminversion formulaMellin transformBessel functionsHeisenberg uncertainty principleMathematics Subject Classifications: 42A3844A2026D1033C10 AcknowledgmentsThe authors are grateful to the reviewers for their valuable contributions in improving the paper's readability.Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"inequality for a modified Struve transform","authors":"Selma Negzaoui, Nesrin Yousfi","doi":"10.1080/10652469.2023.2275129","DOIUrl":"https://doi.org/10.1080/10652469.2023.2275129","url":null,"abstract":"AbstractIn this paper, we aim to establish an L2 inequality for a Modified Struve transform of order α, denoted as Sα. For this purpose, we use Titchmarsh's method consisting of applying Mellin transform to invert asymmetrical Fourier transforms. We obtain the inversion formula and the L2 estimation of the Modified Struve transform Sα. As an application, we prove the Heisenberg uncertainty principle for Sα.Keywords: L2 inequalityModified Struve transforminversion formulaMellin transformBessel functionsHeisenberg uncertainty principleMathematics Subject Classifications: 42A3844A2026D1033C10 AcknowledgmentsThe authors are grateful to the reviewers for their valuable contributions in improving the paper's readability.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"39 14","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-02DOI: 10.1080/10652469.2023.2272758
Wissem Benamira, Ahmed Nasri, Fateh Ellaggoune
AbstractThe aim of this research is to present a new generalization of d-orthogonal (d≥2) polynomials of Laguerre type by utilizing a suitable generating function from Sheffer class and employing operational rules associated with the lowering and raising operators that satisfy d-orthogonality. We derive several properties of these polynomials and establish the recurrence relation. Moreover, we provide explicit, connection and inversion formulas, the (d+1)-order differential equation, and the canonical d-dimensional functional vector.Keywords: d-orthogonalityd-orthogonal polynomials of Laguerre typegenerating functionlowering operatorquasi-monomiality principleconnection coefficientsAMS Classifications: 33C4539A7041A5842C05 AcknowledgmentsThe authors thank the referees for their careful reading of the manuscript and for their constructive comments and suggestions.Data availability statementData sharing not applicable to this article as no data sets were generated or analyzed during the current study.Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"Operational rules for a new family of <i>d</i> -orthogonal polynomials of Laguerre type","authors":"Wissem Benamira, Ahmed Nasri, Fateh Ellaggoune","doi":"10.1080/10652469.2023.2272758","DOIUrl":"https://doi.org/10.1080/10652469.2023.2272758","url":null,"abstract":"AbstractThe aim of this research is to present a new generalization of d-orthogonal (d≥2) polynomials of Laguerre type by utilizing a suitable generating function from Sheffer class and employing operational rules associated with the lowering and raising operators that satisfy d-orthogonality. We derive several properties of these polynomials and establish the recurrence relation. Moreover, we provide explicit, connection and inversion formulas, the (d+1)-order differential equation, and the canonical d-dimensional functional vector.Keywords: d-orthogonalityd-orthogonal polynomials of Laguerre typegenerating functionlowering operatorquasi-monomiality principleconnection coefficientsAMS Classifications: 33C4539A7041A5842C05 AcknowledgmentsThe authors thank the referees for their careful reading of the manuscript and for their constructive comments and suggestions.Data availability statementData sharing not applicable to this article as no data sets were generated or analyzed during the current study.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"213 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135974572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.1080/10652469.2023.2272026
Fethi Bouzeffour, Wissem Jedidi
AbstractIn this paper, utilizing the Dunkl transform and a generalized translation operator, we derive an analogue of the Riesz-Feller fractional derivative for a class of functions satisfying Lipschitz conditions.Keywords: Dunkl operatorDunkl transformgeneralized Dunkl translationfractional derivative2010 Mathematics Subject Classifications: 44A3342A3833C67 AcknowledgmentsThe first-named author extends his appreciation to Researchers Supporting Project Number (RSPD2023R974), King Saud University, Riyadh, Saudi Arabia.Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"Fractional Riesz–Feller type derivative for the one dimensional Dunkl operator and Lipschitz condition","authors":"Fethi Bouzeffour, Wissem Jedidi","doi":"10.1080/10652469.2023.2272026","DOIUrl":"https://doi.org/10.1080/10652469.2023.2272026","url":null,"abstract":"AbstractIn this paper, utilizing the Dunkl transform and a generalized translation operator, we derive an analogue of the Riesz-Feller fractional derivative for a class of functions satisfying Lipschitz conditions.Keywords: Dunkl operatorDunkl transformgeneralized Dunkl translationfractional derivative2010 Mathematics Subject Classifications: 44A3342A3833C67 AcknowledgmentsThe first-named author extends his appreciation to Researchers Supporting Project Number (RSPD2023R974), King Saud University, Riyadh, Saudi Arabia.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"68 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-26DOI: 10.1080/10652469.2023.2272212
Yong-Kum Cho, Seok-Young Chung, Young Woong Park
In consideration of the integral transform whose kernel arises as an oscillatory solution of certain second-order linear differential equation, its positivity is investigated on the basis of Sturm's theory. As applications, positivity criteria are obtained for Hankel transforms as well as trigonometric integrals defined on the positive real line.
{"title":"Positivity of oscillatory integrals and Hankel transforms","authors":"Yong-Kum Cho, Seok-Young Chung, Young Woong Park","doi":"10.1080/10652469.2023.2272212","DOIUrl":"https://doi.org/10.1080/10652469.2023.2272212","url":null,"abstract":"In consideration of the integral transform whose kernel arises as an oscillatory solution of certain second-order linear differential equation, its positivity is investigated on the basis of Sturm's theory. As applications, positivity criteria are obtained for Hankel transforms as well as trigonometric integrals defined on the positive real line.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134906997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-26DOI: 10.1080/10652469.2023.2260074
Neila Ben Romdhane, Hana Boukattaya
AbstractConnection between the interlacing of the zeros and the orthogonality of a given sequence of polynomials is done by K. Driver. In this paper, we attempt to extend this result to some particular cases of d-orthogonal polynomials. In fact, first, we characterize the 2-orthogonality of a given sequence {Pn}n≥0, with the existence of a certain ratio cn expressed by means of the zeros of Pn. Then, for the (d+1)-fold symmetric polynomials, {Pn}n≥0, such that Pn has qn distinct positive real zeros, n=(d+1)qn+j,j=0,…,d, we study the connection between the interlacing of these zeros, the d-orthogonality and the positivity of the ratio cn. Finally, we give necessary and sufficient conditions on the zeros of a given sequence {Pn}n≥0, that will assure that this sequence satisfies a particular (d+1)-order recurrence relation. Many examples to illustrate the obtained results are given.KEYWORDS: (d+1)-Fold symmetric polynomialsinterlacing propertyd-orthogonal polynomialsrecurrence relationzeros of polynomialsAMS CLASSIFICATION:: 42C0533C45 AcknowledgmentsThe authors thank the anonymous referees for their helpful comments and suggestions that improved the quality of the manuscript.Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"On connection between zeros and <i>d</i> -orthogonality","authors":"Neila Ben Romdhane, Hana Boukattaya","doi":"10.1080/10652469.2023.2260074","DOIUrl":"https://doi.org/10.1080/10652469.2023.2260074","url":null,"abstract":"AbstractConnection between the interlacing of the zeros and the orthogonality of a given sequence of polynomials is done by K. Driver. In this paper, we attempt to extend this result to some particular cases of d-orthogonal polynomials. In fact, first, we characterize the 2-orthogonality of a given sequence {Pn}n≥0, with the existence of a certain ratio cn expressed by means of the zeros of Pn. Then, for the (d+1)-fold symmetric polynomials, {Pn}n≥0, such that Pn has qn distinct positive real zeros, n=(d+1)qn+j,j=0,…,d, we study the connection between the interlacing of these zeros, the d-orthogonality and the positivity of the ratio cn. Finally, we give necessary and sufficient conditions on the zeros of a given sequence {Pn}n≥0, that will assure that this sequence satisfies a particular (d+1)-order recurrence relation. Many examples to illustrate the obtained results are given.KEYWORDS: (d+1)-Fold symmetric polynomialsinterlacing propertyd-orthogonal polynomialsrecurrence relationzeros of polynomialsAMS CLASSIFICATION:: 42C0533C45 AcknowledgmentsThe authors thank the anonymous referees for their helpful comments and suggestions that improved the quality of the manuscript.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134885390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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