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Integral Transforms and Special Functions最新文献

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The h-Fourier sine-Laplace discrete generalized convolution on time scale 时间尺度上的h-傅里叶正弦拉普拉斯离散广义卷积
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-11-10 DOI: 10.1080/10652469.2022.2142788
Hoang Tung, N. X. Thao, V. Tuan
{"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}
引用次数: 0
Weighted integrability of Fourier–Jacobi transforms 傅里叶-雅可比变换的加权可积性
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-11-08 DOI: 10.1080/10652469.2022.2140801
S. Volosivets
{"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}
引用次数: 1
Upper bounds and asymptotic expansion for Macdonald's function and the summability of the Kontorovich-Lebedev integrals Macdonald函数的上界和渐近展开式及Kontorovich-Ledev积分的可和性
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-11-07 DOI: 10.1080/10652469.2023.2190590
S. Yakubovich
{"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}
引用次数: 0
Characterizations of the gyrator transform via the fractional Fourier transform 利用分数傅立叶变换刻画回转器变换
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-11-04 DOI: 10.1080/10652469.2022.2138868
T. Kagawa, Toshio Suzuki
{"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}
引用次数: 0
Recurrence relation for the Appell sequences appel序列的递推关系
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-11-03 DOI: 10.1080/10652469.2022.2140800
Ghania Guettai, D. Laissaoui, M. Rahmani, Madjid Sebaoui
{"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}
引用次数: 0
A generic inequality for basic special functions 基本特殊函数的一个一般不等式
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-11-02 DOI: 10.1080/10652469.2022.2138379
M. Masjed‐Jamei
{"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}
引用次数: 0
Applications of Caputo operators in the evaluation of Clebsch–Gordan-type multiple elliptic integrals Caputo算子在求解clebsch - gordan型多重椭圆积分中的应用
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-10-09 DOI: 10.1080/10652469.2022.2128798
J. Campbell
{"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}
引用次数: 1
Expressing Hilbert and Riesz transforms in terms of wavelet transforms 用小波变换表示Hilbert和Riesz变换
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-09-25 DOI: 10.1080/10652469.2022.2126465
S. Moritoh, Nao Takemoto
{"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}
引用次数: 1
Division problem of a regular symmetric form the case x 3 u = λxv 在x3u = λxv情况下的正则对称除法问题
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-09-25 DOI: 10.1080/10652469.2022.2125964
M. Mejri, T. Marzouki
{"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}
引用次数: 0
Absolutely convergent Fourier–Jacobi series and generalized Lipschitz classes 绝对收敛的傅里叶-雅可比级数和广义Lipschitz类
IF 1 3区 数学
Integral Transforms and Special Functions Pub Date : 2022-09-19 DOI: 10.1080/10652469.2022.2122460
Faouaz Saadi, R. Daher
{"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}
引用次数: 0
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