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Journal of Pseudo-Differential Operators and Applications最新文献

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The Hartley–Bessel function: product formula and convolution structure 哈特里-贝塞尔函数：乘积公式和卷积结构
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-05-07 DOI: 10.1007/s11868-024-00610-5
F. Bouzeffour
{"title":"The Hartley–Bessel function: product formula and convolution structure","authors":"F. Bouzeffour","doi":"10.1007/s11868-024-00610-5","DOIUrl":"https://doi.org/10.1007/s11868-024-00610-5","url":null,"abstract":"<p>This paper explores a one-parameter extension of the Hartley kernel expressed as a real combination of two Bessel functions, termed the Hartley–Bessel function. The key feature of the Hartley–Bessel function is derived through a limit transition from the <span>(-1)</span> little Jacobi polynomials. The Hartley–Bessel function emerges as an eigenfunction of a first-order difference-differential operator and possesses a Sonin integral-type representation. Our main contribution lies in investigating anovel product formula for this function, which subsequently facilitates the development of innovative generalized translation and convolution structures on the real line. The obtained product formula is expressed as an integral in terms of this function with an explicit non-positive and uniformly bounded measure. Consequently, a non-positivity-preserving convolution structure is established.\u0000</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888010","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
Quasinormable Fréchet spaces and M. W. Wong’s inequality 类非线性弗雷谢特空间和 M. W. Wong 不等式
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-05-03 DOI: 10.1007/s11868-024-00606-1
Eduard A. Nigsch, Norbert Ortner
{"title":"Quasinormable Fréchet spaces and M. W. Wong’s inequality","authors":"Eduard A. Nigsch, Norbert Ortner","doi":"10.1007/s11868-024-00606-1","DOIUrl":"https://doi.org/10.1007/s11868-024-00606-1","url":null,"abstract":"<p>A short proof of M. W. Wong’s inequality <span>(leftVert J_{-s}varphi rightVert _p le varepsilon leftVert J_{-t}varphi rightVert _p + C leftVert varphi rightVert _p)</span> is given.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881441","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
The general Dabrowski–Sitarz–Zalecki type theorem for odd dimensional manifolds with boundary III 有边界奇维流形的一般达布罗夫斯基-西塔尔兹-扎莱基类型定理 III
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-05-03 DOI: 10.1007/s11868-024-00604-3
Yuchen Yang, Yong Wang
{"title":"The general Dabrowski–Sitarz–Zalecki type theorem for odd dimensional manifolds with boundary III","authors":"Yuchen Yang, Yong Wang","doi":"10.1007/s11868-024-00604-3","DOIUrl":"https://doi.org/10.1007/s11868-024-00604-3","url":null,"abstract":"<p>In this paper, for the Dirac operator and three One-forms we give the proof of the another general Dabrowski–Sitarz–Zalecki type theorem for the spectral Einstein functional on odd dimensional manifolds with boundary.\u0000</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888125","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
Fractional Euclidean bosonic equation via variational 通过变分的分数欧几里得玻色方程
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-05-03 DOI: 10.1007/s11868-024-00611-4
Nemat Nyamoradi, J. Vanterler da C. Sousa
{"title":"Fractional Euclidean bosonic equation via variational","authors":"Nemat Nyamoradi, J. Vanterler da C. Sousa","doi":"10.1007/s11868-024-00611-4","DOIUrl":"https://doi.org/10.1007/s11868-024-00611-4","url":null,"abstract":"<p>In this paper, we study the existence of solutions for the following class of Euclidean bosonic equations with Liouville–Weyl fractional derivatives </p><span>$$begin{aligned} {left{ begin{array}{ll} {_{x}}D_{infty }^{beta }{_{-infty }}D_{x}^{beta }e^{C {_{x}}D_{infty }^{beta }{_{-infty }}D_{x}^{beta }}u = lambda omega (x)u+ Q(x)g(x,u)&amp;{}text{ in },,{mathbb {R}}, uin mathcal {H}_c^{beta ,infty } ({mathbb {R}}), end{array}right. } end{aligned}$$</span><p>where <span>(beta in (0,frac{1}{2}))</span>, <span>({_{-infty }}D_{x}^{beta }u(cdot ), {_{x}}D_{infty }^{beta }u(cdot ))</span> denote the left and right Liouville–Weyl fractional derivatives, <span>(omega ,Q:{mathbb {R}}rightarrow {mathbb {R}})</span> is a positive function with <span>(omega ,Qin L^{frac{1}{2beta }} ({mathbb {R}}))</span> and <span>(g: {mathbb {R}}rightarrow {mathbb {R}})</span> is a continuous function satisfying suitable conditions. Finally, an example is provided.\u0000</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881478","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
Application of Bargmann transform in the study of affine heat kernel transform 巴格曼变换在仿射热核变换研究中的应用
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-04-26 DOI: 10.1007/s11868-024-00603-4
Partha Sarathi Patra, Shubham R. Bais, D. Venku Naidu
{"title":"Application of Bargmann transform in the study of affine heat kernel transform","authors":"Partha Sarathi Patra, Shubham R. Bais, D. Venku Naidu","doi":"10.1007/s11868-024-00603-4","DOIUrl":"https://doi.org/10.1007/s11868-024-00603-4","url":null,"abstract":"<p>Consider the differential operator </p><span>$$begin{aligned} Delta _{a,b} = Big (frac{d^2}{dt^2} + frac{4pi ia}{b}tfrac{d}{dt} - frac{4pi ^2a^2t^2}{b^2} + frac{2pi ia}{b}IBig ), t&gt;0, a,bin {mathbb {R}}, end{aligned}$$</span><p>where <i>I</i> is the identity operator. The operator <span>(Delta _{a,b})</span> is known as affine Laplacian. We consider the heat equation associated to the operator <span>(Delta _{a,b})</span> with initial condition <i>f</i> from <span>(L^2({mathbb {R}}^n))</span>. Its solution is denoted by <span>(e^{tDelta _{a,b}}f)</span>. The transform <span>(f mapsto e^{tDelta _{a,b}}f)</span> is called affine heat kernel transform (or A-heat kernel transform). In this article, we consider (analytically extended) affine heat kernel transform and characterize the image of <span>(displaystyle L^2({mathbb {R}}))</span> under it as a weighted Bergman space of analytic functions on <span>({mathbb {C}})</span> with nonnegative weight. Consequently, we study <span>(L^p)</span>-boundedness of affine heat kernel transform, <span>(L^p)</span>-boundedness of affine Bargmann projection and related duality results. Moreover, we define affine Weyl translations and characterize the maximal and minimal spaces of analytic functions on <span>({mathbb {C}})</span> which are invariant under the affine Weyl translations.</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806442","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
New quadratic phase Wigner distribution and ambiguity function with applications to LFM signals 新的二次相位 Wigner 分布和模糊函数在低频调制信号中的应用
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-04-22 DOI: 10.1007/s11868-024-00609-y
Aamir Hamid Dar, Manal Z. M. Abdalla, M. Y. Bhat, Ahmad Asiri
{"title":"New quadratic phase Wigner distribution and ambiguity function with applications to LFM signals","authors":"Aamir Hamid Dar, Manal Z. M. Abdalla, M. Y. Bhat, Ahmad Asiri","doi":"10.1007/s11868-024-00609-y","DOIUrl":"https://doi.org/10.1007/s11868-024-00609-y","url":null,"abstract":"","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140673225","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
Wave front sets of Riesz type on Minkowski space 闵科夫斯基空间上的里兹型波前集合
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-04-22 DOI: 10.1007/s11868-024-00605-2
Xingya Fan, Jingang Dai, Jianxun He
{"title":"Wave front sets of Riesz type on Minkowski space","authors":"Xingya Fan, Jingang Dai, Jianxun He","doi":"10.1007/s11868-024-00605-2","DOIUrl":"https://doi.org/10.1007/s11868-024-00605-2","url":null,"abstract":"","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140677532","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
The gyrator transform of the generalized functions 广义函数的回旋变换
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-04-22 DOI: 10.1007/s11868-024-00607-0
T. Kagawa, Toshio Suzuki
{"title":"The gyrator transform of the generalized functions","authors":"T. Kagawa, Toshio Suzuki","doi":"10.1007/s11868-024-00607-0","DOIUrl":"https://doi.org/10.1007/s11868-024-00607-0","url":null,"abstract":"","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140673488","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
The heat semigroups and uncertainty principles related to canonical Fourier–Bessel transform 与典型傅立叶-贝塞尔变换有关的热半群和不确定性原理
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-04-22 DOI: 10.1007/s11868-024-00608-z
Sami Ghazouani, J. Sahbani
{"title":"The heat semigroups and uncertainty principles related to canonical Fourier–Bessel transform","authors":"Sami Ghazouani, J. Sahbani","doi":"10.1007/s11868-024-00608-z","DOIUrl":"https://doi.org/10.1007/s11868-024-00608-z","url":null,"abstract":"","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140673840","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
Generalized Pizzetti’s formula for Weinstein operator and its applications 韦恩斯坦算子的广义皮泽蒂公式及其应用
IF 1.1 3区 数学
Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-04-22 DOI: 10.1007/s11868-024-00602-5
F. Bouzeffour, W. Jedidi
{"title":"Generalized Pizzetti’s formula for Weinstein operator and its applications","authors":"F. Bouzeffour, W. Jedidi","doi":"10.1007/s11868-024-00602-5","DOIUrl":"https://doi.org/10.1007/s11868-024-00602-5","url":null,"abstract":"","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140672188","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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