Pseudo-differential operator in the framework of linear canonical transform domain

被引：4
|
作者：
Prasad, Akhilesh [1 ]
Ansari, Z. A. [1 ]
Jain, Pankaj [2 ]
机构：
[1] Indian Sch Mines, Indian Inst Technol, Dept Math & Comp, Dhanbad 826004, India
[2] South Asian Univ, Dept Math, New Delhi 110021, India
来源：
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2021年 / 14卷 / 07期
关键词：
Linear canonical transform; pseudo-differential operator; convolution; Sobolev space; FRACTIONAL FOURIER-TRANSFORM; DISTRIBUTIONS;
D O I：
10.1142/S1793557121501175
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main goal of this paper is to study properties of the linear canonical transform (LCT) on Schwartz-type space S-A(R). The symbol class S-rho,sigma(m,A) is introduced. The pseudodifferential operator (p.d.o.) involving LCT is defined and also some of its properties including boundedness are investigated in Sobolev-type space. Kernel and integral representation of p.d.o. are obtained. Some applications of LCT to generalized partial differential equations and canonical convolution integral equation have been solved.
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页数：18
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