Pub Date : 2022-11-10DOI: 10.1080/10652469.2022.2142788
Hoang Tung, N. X. Thao, V. Tuan
In this paper, we introduce h-Fourier sine-Laplace discrete generalized convolution. We study a class of generalized convolution transforms and give necessary and sufficient conditions so that the transformations are unitary. As application, we obtain solutions in explicit form of some classes of the Toeplitz plus Hankel-type equations related to the h-Fourier sine-Laplace generalized convolution.
{"title":"The h-Fourier sine-Laplace discrete generalized convolution on time scale","authors":"Hoang Tung, N. X. Thao, V. Tuan","doi":"10.1080/10652469.2022.2142788","DOIUrl":"https://doi.org/10.1080/10652469.2022.2142788","url":null,"abstract":"In this paper, we introduce h-Fourier sine-Laplace discrete generalized convolution. We study a class of generalized convolution transforms and give necessary and sufficient conditions so that the transformations are unitary. As application, we obtain solutions in explicit form of some classes of the Toeplitz plus Hankel-type equations related to the h-Fourier sine-Laplace generalized convolution.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"444 - 456"},"PeriodicalIF":1.0,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42811538","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 : 2022-11-08DOI: 10.1080/10652469.2022.2140801
S. Volosivets
We prove sufficient conditions for the weighted integrability of the Fourier–Jacobi transform. These results generalize a Titchmarsh type result due to Daher and Tyr and also use a generalized Jacobi translation defined by Flensted-Jensen and Koornwinder. Also some results connected with the integrability of Fourier–Jacobi transforms of Jacobi convolutions are given.
{"title":"Weighted integrability of Fourier–Jacobi transforms","authors":"S. Volosivets","doi":"10.1080/10652469.2022.2140801","DOIUrl":"https://doi.org/10.1080/10652469.2022.2140801","url":null,"abstract":"We prove sufficient conditions for the weighted integrability of the Fourier–Jacobi transform. These results generalize a Titchmarsh type result due to Daher and Tyr and also use a generalized Jacobi translation defined by Flensted-Jensen and Koornwinder. Also some results connected with the integrability of Fourier–Jacobi transforms of Jacobi convolutions are given.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"431 - 443"},"PeriodicalIF":1.0,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42939132","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 : 2022-11-07DOI: 10.1080/10652469.2023.2190590
S. Yakubovich
Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function . The results can be applied, for instance, to study the summability of the divergent Kontorovich-Lebedev integrals in the sense of Jones. Namely, we answer affirmatively a question (cf. [Ehrenmark U. Summability experiments with a class of divergent inverse Kontorovich-Lebedev transforms. Comput Math Appl. 2018;76(1):141–154.]) whether these integrals converge for even entire functions of the exponential type in a weak sense.
建立了Macdonald函数的一致上界和具有显式余项的渐近展开式。这些结果可以应用于研究Jones意义下的发散Kontorovich-Lebedev积分的可和性。也就是说，我们肯定地回答了一个问题（参见[Ehrenmark U.用一类发散逆Kontorovich Lebedev变换进行的可和性实验。Comput Math Appl.2018；76（1）:141–154.]），这些积分是否在弱意义上收敛于甚至整个指数型函数。
{"title":"Upper bounds and asymptotic expansion for Macdonald's function and the summability of the Kontorovich-Lebedev integrals","authors":"S. Yakubovich","doi":"10.1080/10652469.2023.2190590","DOIUrl":"https://doi.org/10.1080/10652469.2023.2190590","url":null,"abstract":"Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function . The results can be applied, for instance, to study the summability of the divergent Kontorovich-Lebedev integrals in the sense of Jones. Namely, we answer affirmatively a question (cf. [Ehrenmark U. Summability experiments with a class of divergent inverse Kontorovich-Lebedev transforms. Comput Math Appl. 2018;76(1):141–154.]) whether these integrals converge for even entire functions of the exponential type in a weak sense.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"721 - 736"},"PeriodicalIF":1.0,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41376977","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 : 2022-11-04DOI: 10.1080/10652469.2022.2138868
T. Kagawa, Toshio Suzuki
ABSTRACT In this note, we will explain the relationship between the fractional Fourier transform and the gyrator transform. In particular, we will show the properties of the gyrator transform, which is getting the eigenfunction and eigenvalue of the gyrator transform, recursion formula, the relation between the Wigner distribution and the gyrator transform, the differential equation satisfied with the gyrator transform of some functions, and the representation of the gyrator transform as the self-adjoint operator. Moreover, we will consider the generalized gyrator transform of tempered distributions.
{"title":"Characterizations of the gyrator transform via the fractional Fourier transform","authors":"T. Kagawa, Toshio Suzuki","doi":"10.1080/10652469.2022.2138868","DOIUrl":"https://doi.org/10.1080/10652469.2022.2138868","url":null,"abstract":"ABSTRACT In this note, we will explain the relationship between the fractional Fourier transform and the gyrator transform. In particular, we will show the properties of the gyrator transform, which is getting the eigenfunction and eigenvalue of the gyrator transform, recursion formula, the relation between the Wigner distribution and the gyrator transform, the differential equation satisfied with the gyrator transform of some functions, and the representation of the gyrator transform as the self-adjoint operator. Moreover, we will consider the generalized gyrator transform of tempered distributions.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"399 - 413"},"PeriodicalIF":1.0,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44008799","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 : 2022-11-03DOI: 10.1080/10652469.2022.2140800
Ghania Guettai, D. Laissaoui, M. Rahmani, Madjid Sebaoui
In this paper, we present several explicit formulas for Appell polynomials in terms of the weighted Stirling numbers of the second kind. We also provide a unified approach to obtain a three-term recurrence formula for the computation of Appell polynomials. Several examples are given to illustrate our results. As an application, we define and study a new class of polynomials that we call SPI polynomials. They are related to sums of powers of integers.
{"title":"Recurrence relation for the Appell sequences","authors":"Ghania Guettai, D. Laissaoui, M. Rahmani, Madjid Sebaoui","doi":"10.1080/10652469.2022.2140800","DOIUrl":"https://doi.org/10.1080/10652469.2022.2140800","url":null,"abstract":"In this paper, we present several explicit formulas for Appell polynomials in terms of the weighted Stirling numbers of the second kind. We also provide a unified approach to obtain a three-term recurrence formula for the computation of Appell polynomials. Several examples are given to illustrate our results. As an application, we define and study a new class of polynomials that we call SPI polynomials. They are related to sums of powers of integers.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"414 - 429"},"PeriodicalIF":1.0,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44989666","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 : 2022-11-02DOI: 10.1080/10652469.2022.2138379
M. Masjed‐Jamei
We introduce a generic inequality of the form and show that many special functions such as gamma and polygamma functions, Riemann zeta function, beta and incomplete beta functions, Gauss and confluent hypergeometric functions, elliptic integrals and error function satisfy such type of the inequality. We also obtain new inequalities of this type for inverse trigonometric functions and .
{"title":"A generic inequality for basic special functions","authors":"M. Masjed‐Jamei","doi":"10.1080/10652469.2022.2138379","DOIUrl":"https://doi.org/10.1080/10652469.2022.2138379","url":null,"abstract":"We introduce a generic inequality of the form and show that many special functions such as gamma and polygamma functions, Riemann zeta function, beta and incomplete beta functions, Gauss and confluent hypergeometric functions, elliptic integrals and error function satisfy such type of the inequality. We also obtain new inequalities of this type for inverse trigonometric functions and .","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"384 - 398"},"PeriodicalIF":1.0,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48418110","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 : 2022-10-09DOI: 10.1080/10652469.2022.2128798
J. Campbell
We apply a method of semi-integration by parts (SIBP) that we had previously derived and formulated using the semi-derivative and semi-primitive operators. We obtain many new results on integrals involving the complete elliptic integrals as integrand factors, building on the work of Glasser, Cantarini, Wan, and Zhou. Our main results have not appeared in past literature concerning integrals involving products of the complete elliptic integral(s) of the first and/or second kinds. Furthermore, many previously known identities for such integrals are special cases of our SIBP identity for analytic functions.
{"title":"Applications of Caputo operators in the evaluation of Clebsch–Gordan-type multiple elliptic integrals","authors":"J. Campbell","doi":"10.1080/10652469.2022.2128798","DOIUrl":"https://doi.org/10.1080/10652469.2022.2128798","url":null,"abstract":"We apply a method of semi-integration by parts (SIBP) that we had previously derived and formulated using the semi-derivative and semi-primitive operators. We obtain many new results on integrals involving the complete elliptic integrals as integrand factors, building on the work of Glasser, Cantarini, Wan, and Zhou. Our main results have not appeared in past literature concerning integrals involving products of the complete elliptic integral(s) of the first and/or second kinds. Furthermore, many previously known identities for such integrals are special cases of our SIBP identity for analytic functions.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"371 - 383"},"PeriodicalIF":1.0,"publicationDate":"2022-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43220278","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 : 2022-09-25DOI: 10.1080/10652469.2022.2126465
S. Moritoh, Nao Takemoto
ABSTRACT An alternative wavelet inversion formula was considered by Lebedeva and Postnikov in 2014. The main aim of the paper is to give a multidimensional version of their formula; the Hilbert and Riesz transforms of functions are expressed in terms of the wavelet transforms.
{"title":"Expressing Hilbert and Riesz transforms in terms of wavelet transforms","authors":"S. Moritoh, Nao Takemoto","doi":"10.1080/10652469.2022.2126465","DOIUrl":"https://doi.org/10.1080/10652469.2022.2126465","url":null,"abstract":"ABSTRACT An alternative wavelet inversion formula was considered by Lebedeva and Postnikov in 2014. The main aim of the paper is to give a multidimensional version of their formula; the Hilbert and Riesz transforms of functions are expressed in terms of the wavelet transforms.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"365 - 370"},"PeriodicalIF":1.0,"publicationDate":"2022-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42978396","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 : 2022-09-25DOI: 10.1080/10652469.2022.2125964
M. Mejri, T. Marzouki
ABSTRACT We study the following problem: given a regular symmetric form (linear functional) v, find all the regular symmetric forms u which satisfy the equation . We give the second-order recurrence relation of the orthogonal polynomial sequence with respect to u. Moreover, in the case where v is a semi-classical form of class s, we show that u is semi-classical and its class is analyzed in term of the class of v. An example is highlighted.
{"title":"Division problem of a regular symmetric form the case x 3 u = λxv","authors":"M. Mejri, T. Marzouki","doi":"10.1080/10652469.2022.2125964","DOIUrl":"https://doi.org/10.1080/10652469.2022.2125964","url":null,"abstract":"ABSTRACT We study the following problem: given a regular symmetric form (linear functional) v, find all the regular symmetric forms u which satisfy the equation . We give the second-order recurrence relation of the orthogonal polynomial sequence with respect to u. Moreover, in the case where v is a semi-classical form of class s, we show that u is semi-classical and its class is analyzed in term of the class of v. An example is highlighted.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"346 - 363"},"PeriodicalIF":1.0,"publicationDate":"2022-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46511762","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 : 2022-09-19DOI: 10.1080/10652469.2022.2122460
Faouaz Saadi, R. Daher
In this paper, we give necessary and sufficient conditions in terms of Fourier–Jacobi coefficients of a function f, to ensure that f belongs either to one of the generalized Lipschitz classes and for and . Also a condition for generalized Jacobi differentiability of a function on interval is proved.
{"title":"Absolutely convergent Fourier–Jacobi series and generalized Lipschitz classes","authors":"Faouaz Saadi, R. Daher","doi":"10.1080/10652469.2022.2122460","DOIUrl":"https://doi.org/10.1080/10652469.2022.2122460","url":null,"abstract":"In this paper, we give necessary and sufficient conditions in terms of Fourier–Jacobi coefficients of a function f, to ensure that f belongs either to one of the generalized Lipschitz classes and for and . Also a condition for generalized Jacobi differentiability of a function on interval is proved.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"334 - 345"},"PeriodicalIF":1.0,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46449834","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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