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On the generalisation of Henstock-Kurzweil Fourier transform 关于Henstock-Kurzweil傅立叶变换的推广
Journal of classical analysis Pub Date : 2022-02-21 DOI: 10.7153/jca-2022-20-09
S. Mahanta, S. Ray
{"title":"On the generalisation of Henstock-Kurzweil Fourier transform","authors":"S. Mahanta, S. Ray","doi":"10.7153/jca-2022-20-09","DOIUrl":"https://doi.org/10.7153/jca-2022-20-09","url":null,"abstract":"In this paper, a generalised integral called the Laplace integral is defined on unbounded intervals, and some of its properties, including necessary and sufficient condition for differentiating under the integral sign, are discussed. It is also shown that this integral is more general than the Henstock-Kurzweil integral. Finally, the Fourier transform is defined using the Laplace integral, and its well-known properties are established.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42074451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Fourier transform inversion in the Alexiewicz norm Alexewicz范数中的傅立叶变换反演
Journal of classical analysis Pub Date : 2022-02-03 DOI: 10.7153/jca-2022-19-07
E. Talvila
{"title":"Fourier transform inversion in the Alexiewicz norm","authors":"E. Talvila","doi":"10.7153/jca-2022-19-07","DOIUrl":"https://doi.org/10.7153/jca-2022-19-07","url":null,"abstract":"Abstract. If f P LpRq it is proved that limSÑ8‖f ́ f ̊ DS‖ “ 0, where DSpxq “ sinpSxq{pπxq is the Dirichlet kernel and ‖f‖ “ supαăβ | şβ α fpxq dx| is the Alexiewicz norm. This gives a symmetric inversion of the Fourier transform on the real line. An asymmetric inversion is also proved. The results also hold for a measure given by dF where F is a continuous function of bounded variation. Such measures need not be absolutely continuous with respect to Lebesgue measure. An example shows there is f P LpRq such that limSÑ8‖f ́ f ̊ DS‖1‰ 0.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42447787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Refined normal approximations for the Student distribution 学生分布的精细正态近似
Journal of classical analysis Pub Date : 2022-01-16 DOI: 10.7153/jca-2022-20-03
Frédéric Ouimet
{"title":"Refined normal approximations for the Student distribution","authors":"Frédéric Ouimet","doi":"10.7153/jca-2022-20-03","DOIUrl":"https://doi.org/10.7153/jca-2022-20-03","url":null,"abstract":"In this paper, we develop a local limit theorem for the Student distribution. We use it to improve the normal approximation of the Student survival function given in Shafiei & Saberali (2015) and to derive asymptotic bounds for the corresponding maximal errors at four levels of approximation. As a corollary, approximations for the percentage points (or quantiles) of the Student distribution are obtained in terms of the percentage points of the standard normal distribution.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44862341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations in terms of (p,q)-order (p,q)阶齐次和非齐次线性差分方程亚纯解的增长
Journal of classical analysis Pub Date : 2022-01-05 DOI: 10.7153/jca-2023-21-07
C. Ghosh, Subhadip Khan, A. Bandyopadhyay
{"title":"On the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations in terms of (p,q)-order","authors":"C. Ghosh, Subhadip Khan, A. Bandyopadhyay","doi":"10.7153/jca-2023-21-07","DOIUrl":"https://doi.org/10.7153/jca-2023-21-07","url":null,"abstract":"In this paper we have studied the growth of meromorphic solutions of higher order homogeneous and non-homogeneous linear difference equations with entire and meromorphic coefficients. We have extended and improved some results of Zhou and Zheng (2017), Belaidi and Benkarouba (2019) by using (p,q)-order and (p,q)-type.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43837315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Uniqueness of non-homogeneous differential polynomials of meromorphic functions sharing a small function 共享一个小函数的亚纯函数的非齐次微分多项式的唯一性
Journal of classical analysis Pub Date : 2022-01-01 DOI: 10.7153/jca-2022-19-06
D. C. Pramanik, Jayanta Roy
{"title":"Uniqueness of non-homogeneous differential polynomials of meromorphic functions sharing a small function","authors":"D. C. Pramanik, Jayanta Roy","doi":"10.7153/jca-2022-19-06","DOIUrl":"https://doi.org/10.7153/jca-2022-19-06","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit expressions for some linear Euler-type sums containing harmonic and skew-harmonic numbers 若干含调和数和偏调和数的线性欧拉型和的显式表达式
Journal of classical analysis Pub Date : 2022-01-01 DOI: 10.7153/jca-2022-20-07
Ting Zhu
{"title":"Explicit expressions for some linear Euler-type sums containing harmonic and skew-harmonic numbers","authors":"Ting Zhu","doi":"10.7153/jca-2022-20-07","DOIUrl":"https://doi.org/10.7153/jca-2022-20-07","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coefficient problems of a class of q-starlike functions associated with q-analogue of Al-Oboudi-Al-Qahtani integral operator and nephroid domain 一类q-星形函数与Al-Oboudi-Al-Qahtani积分算子的q-拟合及类内域的系数问题
Journal of classical analysis Pub Date : 2022-01-01 DOI: 10.7153/jca-2022-20-04
A. Lasode, T. Opoola
{"title":"Coefficient problems of a class of q-starlike functions associated with q-analogue of Al-Oboudi-Al-Qahtani integral operator and nephroid domain","authors":"A. Lasode, T. Opoola","doi":"10.7153/jca-2022-20-04","DOIUrl":"https://doi.org/10.7153/jca-2022-20-04","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Path connectedness of Volterra type integral operators on Bergman and Dirichlet type spaces Bergman和Dirichlet型空间上Volterra型积分算子的路径连通性
Journal of classical analysis Pub Date : 2022-01-01 DOI: 10.7153/jca-2022-20-05
Cui Wang
{"title":"Path connectedness of Volterra type integral operators on Bergman and Dirichlet type spaces","authors":"Cui Wang","doi":"10.7153/jca-2022-20-05","DOIUrl":"https://doi.org/10.7153/jca-2022-20-05","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the location of zeros of quasi-orthogonal polynomials with applications to some real self-reciprocal polynomials 拟正交多项式的零点定位及其在实自倒易多项式中的应用
Journal of classical analysis Pub Date : 2022-01-01 DOI: 10.7153/jca-2022-19-08
V. Botta, Mijael Hancco Suni
{"title":"On the location of zeros of quasi-orthogonal polynomials with applications to some real self-reciprocal polynomials","authors":"V. Botta, Mijael Hancco Suni","doi":"10.7153/jca-2022-19-08","DOIUrl":"https://doi.org/10.7153/jca-2022-19-08","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Location of zeros of Lacunary-type polynomials in annular regions 环形区域中空洞型多项式零点的定位
Journal of classical analysis Pub Date : 2022-01-01 DOI: 10.7153/jca-2022-20-08
I. A. Wani, Mohammad Hedayetullah Mir, I. Nazir
{"title":"Location of zeros of Lacunary-type polynomials in annular regions","authors":"I. A. Wani, Mohammad Hedayetullah Mir, I. Nazir","doi":"10.7153/jca-2022-20-08","DOIUrl":"https://doi.org/10.7153/jca-2022-20-08","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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