Pub Date : 2022-09-12DOI: 10.1080/10652469.2022.2117807
Yu. A. Brychkov, N. Savischenko
ABSTRACT Some new relations for the confluent Horn functions , and are obtained including differentiation and integration formulas, series and reduction formulas. Some generating functions for various special functions are given in terms of these Horn functions.
{"title":"On some formulas for the confluent Horn functions H3 (c) (a, b, c; d; w, z), H4 (c) (a, c; d; w, z) and H9 (c) (a, b; c; w, z)","authors":"Yu. A. Brychkov, N. Savischenko","doi":"10.1080/10652469.2022.2117807","DOIUrl":"https://doi.org/10.1080/10652469.2022.2117807","url":null,"abstract":"ABSTRACT Some new relations for the confluent Horn functions , and are obtained including differentiation and integration formulas, series and reduction formulas. Some generating functions for various special functions are given in terms of these Horn functions.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"275 - 294"},"PeriodicalIF":1.0,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42418040","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 : 2022-09-12DOI: 10.1080/10652469.2022.2118738
Yu. A. Brychkov, P. Sofotasios
Various relations including differentiation formulas, connection with hypergeometric functions, integral representations, formulas of summation and series representations for three types of Neumann polynomials are derived.
推导了三类诺伊曼多项式的各种关系，包括微分公式、与超几何函数的联系、积分表示、求和公式和级数表示。
{"title":"On some properties of the Neumann polynomials","authors":"Yu. A. Brychkov, P. Sofotasios","doi":"10.1080/10652469.2022.2118738","DOIUrl":"https://doi.org/10.1080/10652469.2022.2118738","url":null,"abstract":"Various relations including differentiation formulas, connection with hypergeometric functions, integral representations, formulas of summation and series representations for three types of Neumann polynomials are derived.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"316 - 333"},"PeriodicalIF":1.0,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46011738","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 : 2022-09-12DOI: 10.1080/10652469.2022.2118737
A. Prasad, Amit Kumar
The main objective of this paper is to enrich the theoretical system of the linear canonical Fourier transform (LCFT) by introducing the canonical potential and corresponding -Sobolev space. Moreover, the Schwartz-type space is introduced. Further, pseudo-differential operator (PDO) is defined and obtained its another integral representation. The -boundedness result for the pseudo-differential operator associated with the LCFT is discussed. Some applications of Sobolev-type spaces and are given.
{"title":"Canonical potential and Lp-Sobolev space involving linear canonical Fourier transform","authors":"A. Prasad, Amit Kumar","doi":"10.1080/10652469.2022.2118737","DOIUrl":"https://doi.org/10.1080/10652469.2022.2118737","url":null,"abstract":"The main objective of this paper is to enrich the theoretical system of the linear canonical Fourier transform (LCFT) by introducing the canonical potential and corresponding -Sobolev space. Moreover, the Schwartz-type space is introduced. Further, pseudo-differential operator (PDO) is defined and obtained its another integral representation. The -boundedness result for the pseudo-differential operator associated with the LCFT is discussed. Some applications of Sobolev-type spaces and are given.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"295 - 315"},"PeriodicalIF":1.0,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46091228","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 : 2022-09-02DOI: 10.1080/10652469.2022.2026351
T. Peachey
Determination of the operator norm for the Laplace transformation, when operating on Lebesgue spaces, is a long unsolved problem. Recently Setterqvist gave an improved bound to that norm. This note shows how his result relates to a more general theorem, which also gives a related reverse inequality, and some other results of Hardy, Littlewood and Pólya.
{"title":"A note on the operator norm of the Laplace transformation","authors":"T. Peachey","doi":"10.1080/10652469.2022.2026351","DOIUrl":"https://doi.org/10.1080/10652469.2022.2026351","url":null,"abstract":"Determination of the operator norm for the Laplace transformation, when operating on Lebesgue spaces, is a long unsolved problem. Recently Setterqvist gave an improved bound to that norm. This note shows how his result relates to a more general theorem, which also gives a related reverse inequality, and some other results of Hardy, Littlewood and Pólya.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"33 1","pages":"711 - 714"},"PeriodicalIF":1.0,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41909204","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 : 2022-08-28DOI: 10.1080/10652469.2022.2116019
F. Soltani, S. Aledawish
In this paper, using the generalized Whittaker translation established by Sousa et al., we shall prove a generalization version of Titchmarsh's theorem for the modified Whittaker transform for functions satisfying the Whittaker-Lipschitz condition in the appropriate space .
{"title":"Generalization of Titchmarsh's theorem for the modified Whittaker transform","authors":"F. Soltani, S. Aledawish","doi":"10.1080/10652469.2022.2116019","DOIUrl":"https://doi.org/10.1080/10652469.2022.2116019","url":null,"abstract":"In this paper, using the generalized Whittaker translation established by Sousa et al., we shall prove a generalization version of Titchmarsh's theorem for the modified Whittaker transform for functions satisfying the Whittaker-Lipschitz condition in the appropriate space .","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"261 - 273"},"PeriodicalIF":1.0,"publicationDate":"2022-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43476781","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 : 2022-08-18DOI: 10.1080/10652469.2022.2111420
A. Abilassan, J. Restrepo, D. Suragan
By using the Laplace transform method, we revisit the multivariate Mittag-Leffler function as an effective tool to construct a solution for some classes of fractional differential equations with constant coefficients. To support our results, we discuss several particular cases related to classical fractional differential operators. The techniques are not only restricted to fractional derivative operators but also can be applied to general constant coefficient differential equations, including high-order ordinary differential equations.
{"title":"On a variant of multivariate Mittag-Leffler's function arising in the Laplace transform method","authors":"A. Abilassan, J. Restrepo, D. Suragan","doi":"10.1080/10652469.2022.2111420","DOIUrl":"https://doi.org/10.1080/10652469.2022.2111420","url":null,"abstract":"By using the Laplace transform method, we revisit the multivariate Mittag-Leffler function as an effective tool to construct a solution for some classes of fractional differential equations with constant coefficients. To support our results, we discuss several particular cases related to classical fractional differential operators. The techniques are not only restricted to fractional derivative operators but also can be applied to general constant coefficient differential equations, including high-order ordinary differential equations.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"244 - 260"},"PeriodicalIF":1.0,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46357834","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 : 2022-08-12DOI: 10.1080/10652469.2022.2108419
F. Bouzeffour, W. Jedidi
ABSTRACT For a class of even weight functions, generalizations of the classical Jacobi and Laguerre polynomials are defined via fractional Rodrigues' type formulas using the Bessel operators in the form . Their properties, including hypergeometric representation, differential recurrence relations and fractional boundary value problem, are investigated.
{"title":"Jacobi-type functions defined by fractional Bessel derivatives","authors":"F. Bouzeffour, W. Jedidi","doi":"10.1080/10652469.2022.2108419","DOIUrl":"https://doi.org/10.1080/10652469.2022.2108419","url":null,"abstract":"ABSTRACT For a class of even weight functions, generalizations of the classical Jacobi and Laguerre polynomials are defined via fractional Rodrigues' type formulas using the Bessel operators in the form . Their properties, including hypergeometric representation, differential recurrence relations and fractional boundary value problem, are investigated.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"228 - 243"},"PeriodicalIF":1.0,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45221138","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 : 2022-08-06DOI: 10.1080/10652469.2022.2105323
S. Georgiev, V. Darvish
In this paper, we deduct some properties of the Fourier transform on arbitrary time scales. We define the generalized shifting problem and we prove the existence of solutions. We define a generalized convolution on anarbitrary time scale and we deduct and prove the generalized convolution theorem.
{"title":"The generalized Fourier convolution on time scales","authors":"S. Georgiev, V. Darvish","doi":"10.1080/10652469.2022.2105323","DOIUrl":"https://doi.org/10.1080/10652469.2022.2105323","url":null,"abstract":"In this paper, we deduct some properties of the Fourier transform on arbitrary time scales. We define the generalized shifting problem and we prove the existence of solutions. We define a generalized convolution on anarbitrary time scale and we deduct and prove the generalized convolution theorem.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"211 - 227"},"PeriodicalIF":1.0,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48265917","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 : 2022-07-22DOI: 10.1080/10652469.2022.2098955
Chelo Ferreira, J. López, Ester Pérez Sinusía
ABSTRACT A modification of Watson's lemma for Laplace transforms was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms for large and that are also convergent. The expansions of are accompanied by error bounds. Asymptotic and convergent expansions of some special functions are given as illustration.
{"title":"A convergent version of Watson's lemma for double integrals","authors":"Chelo Ferreira, J. López, Ester Pérez Sinusía","doi":"10.1080/10652469.2022.2098955","DOIUrl":"https://doi.org/10.1080/10652469.2022.2098955","url":null,"abstract":"ABSTRACT A modification of Watson's lemma for Laplace transforms was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms for large and that are also convergent. The expansions of are accompanied by error bounds. Asymptotic and convergent expansions of some special functions are given as illustration.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"196 - 210"},"PeriodicalIF":1.0,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47542680","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 : 2022-07-19DOI: 10.1080/10652469.2022.2093870
Q. Feng, S. Yuan
In this paper, two types of fractional Fourier–Laplace convolutions are defined, and the corresponding fractional Fourier–Laplace convolution theorems associated with the fractional cosine transform (FRCT), fractional sine transform (FRST) and Laplace transform (LP) are investigated in detail. The relationship between the fractional Fourier–Laplace convolutions and the existing convolutions is given, and Young's type theorem as well as the weighted convolution inequality are also obtained. As an application for fractional Fourier–Laplace convolution, the filter design and the system of convolution-type integral equations are also considered, the computational complexity for the multiplicative filter is analysed, and explicit solutions for these equations are obtained.
{"title":"The explicit solutions for a class of fractional Fourier–Laplace convolution equations","authors":"Q. Feng, S. Yuan","doi":"10.1080/10652469.2022.2093870","DOIUrl":"https://doi.org/10.1080/10652469.2022.2093870","url":null,"abstract":"In this paper, two types of fractional Fourier–Laplace convolutions are defined, and the corresponding fractional Fourier–Laplace convolution theorems associated with the fractional cosine transform (FRCT), fractional sine transform (FRST) and Laplace transform (LP) are investigated in detail. The relationship between the fractional Fourier–Laplace convolutions and the existing convolutions is given, and Young's type theorem as well as the weighted convolution inequality are also obtained. As an application for fractional Fourier–Laplace convolution, the filter design and the system of convolution-type integral equations are also considered, the computational complexity for the multiplicative filter is analysed, and explicit solutions for these equations are obtained.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"128 - 144"},"PeriodicalIF":1.0,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48593304","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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