Pub Date : 2023-03-07DOI: 10.1080/10652469.2023.2182777
Ó. Ciaurri, J. Mínguez Ceniceros, J. Rodríguez
In this paper, we show a complete characterization of the uniform boundedness of the partial sum operator in a discrete Sobolev space with Jacobi measure. As a consequence, we obtain the convergence of the Fourier series. Moreover it is showed that this Sobolev space is the first category which implies that it is not possible to apply the Banach–Steinhaus theorem.
{"title":"On convergence of Fourier series in discrete Jacobi–Sobolev spaces","authors":"Ó. Ciaurri, J. Mínguez Ceniceros, J. Rodríguez","doi":"10.1080/10652469.2023.2182777","DOIUrl":"https://doi.org/10.1080/10652469.2023.2182777","url":null,"abstract":"In this paper, we show a complete characterization of the uniform boundedness of the partial sum operator in a discrete Sobolev space with Jacobi measure. As a consequence, we obtain the convergence of the Fourier series. Moreover it is showed that this Sobolev space is the first category which implies that it is not possible to apply the Banach–Steinhaus theorem.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"703 - 720"},"PeriodicalIF":1.0,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46578021","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 : 2023-03-06DOI: 10.1080/10652469.2023.2182776
T. Tuan, V. Tuan
In this paper, we obtain some Young type inequalities for a polyconvolution and a generalized convolution involving the Fourier-cosine and Fourier-sine integral transforms.
{"title":"Young inequalities for a Fourier cosine and sine polyconvolution and a generalized convolution","authors":"T. Tuan, V. Tuan","doi":"10.1080/10652469.2023.2182776","DOIUrl":"https://doi.org/10.1080/10652469.2023.2182776","url":null,"abstract":"In this paper, we obtain some Young type inequalities for a polyconvolution and a generalized convolution involving the Fourier-cosine and Fourier-sine integral transforms.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"690 - 702"},"PeriodicalIF":1.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41707231","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 : 2023-03-01DOI: 10.1080/10652469.2023.2180502
H. Cohl, Lisa Ritter
ABSTRACT By using the three-term recurrence relation for orthogonal polynomials, we produce a collection of two-dimensional contiguous relations for certain generalized hypergeometric functions. These generalized hypergeometric functions arise through linearization coefficients for some classical orthogonal polynomials in the Askey-scheme, namely Gegenbauer (ultraspherical), Hermite, Jacobi and Laguerre polynomials.
{"title":"Two-dimensional contiguous relations for the linearization coefficients of classical orthogonal polynomials","authors":"H. Cohl, Lisa Ritter","doi":"10.1080/10652469.2023.2180502","DOIUrl":"https://doi.org/10.1080/10652469.2023.2180502","url":null,"abstract":"ABSTRACT By using the three-term recurrence relation for orthogonal polynomials, we produce a collection of two-dimensional contiguous relations for certain generalized hypergeometric functions. These generalized hypergeometric functions arise through linearization coefficients for some classical orthogonal polynomials in the Askey-scheme, namely Gegenbauer (ultraspherical), Hermite, Jacobi and Laguerre polynomials.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"635 - 658"},"PeriodicalIF":1.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45816441","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 : 2023-02-20DOI: 10.1080/10652469.2023.2177846
Ashish Pathak, Shrish Pandey
In the present paper, we define Besov type spaces associated with the Kontorovich–Lebedev transform. We widen the concept of continuous Kontorovich–Lebedev wavelet transform on space and derive continuity of Kontorovich–Lebedev wavelet transform on Besov type spaces and lastly characterize the Besov Kontorovich–Lebedev space by using Kontorovich–Lebedev wavelet coefficients.
{"title":"Kontorovich–Lebedev wavelet transform on Besov type spaces","authors":"Ashish Pathak, Shrish Pandey","doi":"10.1080/10652469.2023.2177846","DOIUrl":"https://doi.org/10.1080/10652469.2023.2177846","url":null,"abstract":"In the present paper, we define Besov type spaces associated with the Kontorovich–Lebedev transform. We widen the concept of continuous Kontorovich–Lebedev wavelet transform on space and derive continuity of Kontorovich–Lebedev wavelet transform on Besov type spaces and lastly characterize the Besov Kontorovich–Lebedev space by using Kontorovich–Lebedev wavelet coefficients.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"659 - 674"},"PeriodicalIF":1.0,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48166251","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 : 2023-02-13DOI: 10.1080/10652469.2023.2176488
F. Soltani, Hanen Saadi
In 1961, Bargmann introduced the classical Segal–Bargmann transform and in 1984, Cholewinsky introduced the generalized Segal–Bargmann transform. These two transforms are the aim of many works, and have many applications in mathematics. In this paper, we introduce the Weinstein-type Segal–Bargmann transform ; and we prove for this transform Plancherel and inversion formulas. Next, we give a relation between the transform and the Weinstein transform in . As applications, we establish a local-type uncertainty inequalities (two versions) and a dispersion inequality for .
{"title":"Inversion formula and uncertainty inequalities for the Weinstein-type Segal–Bargmann transform","authors":"F. Soltani, Hanen Saadi","doi":"10.1080/10652469.2023.2176488","DOIUrl":"https://doi.org/10.1080/10652469.2023.2176488","url":null,"abstract":"In 1961, Bargmann introduced the classical Segal–Bargmann transform and in 1984, Cholewinsky introduced the generalized Segal–Bargmann transform. These two transforms are the aim of many works, and have many applications in mathematics. In this paper, we introduce the Weinstein-type Segal–Bargmann transform ; and we prove for this transform Plancherel and inversion formulas. Next, we give a relation between the transform and the Weinstein transform in . As applications, we establish a local-type uncertainty inequalities (two versions) and a dispersion inequality for .","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"619 - 634"},"PeriodicalIF":1.0,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49137147","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 : 2023-02-04DOI: 10.1080/10652469.2022.2149961
Slobodan Trickovic, M. Stankovic
We derive explicit closed-form formulas for the standard Clausen functions and in terms of the Hurwitz zeta function, where m is a positive integer.
我们导出了标准克劳森函数和Hurwitz zeta函数的显式闭式公式，其中m是正整数。
{"title":"On the closed form of Clausen functions","authors":"Slobodan Trickovic, M. Stankovic","doi":"10.1080/10652469.2022.2149961","DOIUrl":"https://doi.org/10.1080/10652469.2022.2149961","url":null,"abstract":"We derive explicit closed-form formulas for the standard Clausen functions and in terms of the Hurwitz zeta function, where m is a positive integer.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"469 - 477"},"PeriodicalIF":1.0,"publicationDate":"2023-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42824423","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 : 2023-01-24DOI: 10.1080/10652469.2023.2169284
B. J. González, E. Negrín
In this paper, by means of the classical inversion formula of the Mellin transform and also by means of a L 2 inversion formula, we obtain corresponding inversion formulae for a Lambert-type integral transform. As a consequence of these results, we consider some class of functions regarding Salem's equivalence to the Riemann hypothesis.
{"title":"Inversion formulae for a Lambert-type transform and the Salem's equivalence to the Riemann hypothesis","authors":"B. J. González, E. Negrín","doi":"10.1080/10652469.2023.2169284","DOIUrl":"https://doi.org/10.1080/10652469.2023.2169284","url":null,"abstract":"In this paper, by means of the classical inversion formula of the Mellin transform and also by means of a L 2 inversion formula, we obtain corresponding inversion formulae for a Lambert-type integral transform. As a consequence of these results, we consider some class of functions regarding Salem's equivalence to the Riemann hypothesis.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"614 - 618"},"PeriodicalIF":1.0,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47472241","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 : 2023-01-16DOI: 10.1080/10652469.2023.2221774
B. Amri
In this paper, a product formula for the one-dimensional -generalized Fourier kernel is given for , a>0 and , extending the special case of [Boubatra MA, Negzaoui S, Sifi M. A new product formula involving Bessel functions. Integral Transforms Spec Funct. 2022;33:247–263.] when , .
{"title":"Product formula for the one-dimensional (k,a)-generalized Fourier kernel","authors":"B. Amri","doi":"10.1080/10652469.2023.2221774","DOIUrl":"https://doi.org/10.1080/10652469.2023.2221774","url":null,"abstract":"In this paper, a product formula for the one-dimensional -generalized Fourier kernel is given for , a>0 and , extending the special case of [Boubatra MA, Negzaoui S, Sifi M. A new product formula involving Bessel functions. Integral Transforms Spec Funct. 2022;33:247–263.] when , .","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"849 - 860"},"PeriodicalIF":1.0,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44759803","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 : 2023-01-11DOI: 10.1080/10652469.2023.2164889
S. K. Upadhyay, K. Mishra
{"title":"The continuous fractional Bessel wavelet transform and its applications","authors":"S. K. Upadhyay, K. Mishra","doi":"10.1080/10652469.2023.2164889","DOIUrl":"https://doi.org/10.1080/10652469.2023.2164889","url":null,"abstract":"","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44464106","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 : 2023-01-10DOI: 10.1080/10652469.2022.2164277
N. B. Salem
ABSTRACT The objective of this paper is to extend some weighted inequalities for the Weinstein transform. Especially, we are interesting in the study of the Beckner logarithmic inequality, the Shannon inequality. We give a sharp version of this inequality. Next, we establish different Sobolev type embedding theorems in our context. Finally, we deal with some uncertainty inequalities and a logarithmic uncertainty inequality for the Weistein transform.
{"title":"Shannon, Sobolev and uncertainty inequalities for the Weinstein transform","authors":"N. B. Salem","doi":"10.1080/10652469.2022.2164277","DOIUrl":"https://doi.org/10.1080/10652469.2022.2164277","url":null,"abstract":"ABSTRACT The objective of this paper is to extend some weighted inequalities for the Weinstein transform. Especially, we are interesting in the study of the Beckner logarithmic inequality, the Shannon inequality. We give a sharp version of this inequality. Next, we establish different Sobolev type embedding theorems in our context. Finally, we deal with some uncertainty inequalities and a logarithmic uncertainty inequality for the Weistein transform.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"589 - 613"},"PeriodicalIF":1.0,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43636319","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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