Two versions of pseudo-differential operators involving the Kontorovich-Lebedev transform in L2(R+;dx/x)

被引：19

作者：

Prasad, Akhilesh ^{[1
]}

Mandal, Upain K. ^{[1
]}

机构：

[1] Indian Sch Mines, Indian Inst Technol, Dept Appl Math, Dhanbad 826004, Bihar, India

来源：

FORUM MATHEMATICUM | 2018年 / 30卷 / 01期

关键词：

Pseudo-differential operator; Kontorovich-Lebedev transform; Hilbert space; PSEUDO-DIFFERENTIAL OPERATORS; CONVOLUTION;

D O I：

10.1515/forum-2016-0254

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Pseudo-differential operators (p.d.o.) L(x, A(x)) and L (x, A(x)) involving the Kontorovich-Lebedev transform are defined. An estimate for these operators in the Hilbert space L-2 (R+; dx/x) is obtained. A symbol class Lambda is defined and it is shown that the product of any two symbols from this class is again in Lambda. At the end, commutators for the p.d.o. and their boundedness results are discussed.

引用

页码：31 / 42

页数：12

共 10 条

[1] Boundedness of pseudo-differential operators involving Kontorovich-Lebedev transform
Prasad, Akhilesh
Mandal, U. K.
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2017, 28 (04) : 300 - 314
[2] Composition of pseudo-differential operators associated with Kontorovich-Lebedev transform
Prasad, Akhilesh
Mandal, U. K.
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2016, 27 (11) : 878 - 892
[3] ASYMPTOTIC SERIES OF A GENERAL SYMBOL AND PSEUDO-DIFFERENTIAL OPERATORS INVOLVING THE KONTOROVICH-LEBEDEV TRANSFORM
Srivastava, H. M.
Chauhan, Manmohan Singh
Upadhyay, S. K.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2021, 22 (11) : 2461 - 2478
[4] Lαp-boundedness of the pseudo-differential operators associated with the Kontorovich-Lebedev transform
Srivastava, H. M.
Chauhan, Manmohan Singh
Upadhyay, S. K.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2020, 114 (02)
[5] A pair of Kontorovich-Lebedev type transforms and associated pseudo-differential operators
Mandal, U. K.
Prasad, Akhilesh
ANNALS OF MATHEMATICAL SCIENCES AND APPLICATIONS, 2021, 6 (01) : 87 - 118
[6] A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L2a(R+;ma(x)dx)
Maan, Jeetendrasingh
Prasad, Akhilesh
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2024, 40 (06) : 1420 - 1430
[7] ELLIPTICITY AND FREDHOLMNESS OF PSEUDO-DIFFERENTIAL OPERATORS ON l2(Zn)
Dasgupta, Aparajita
Kumar, Vishvesh
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150 (07) : 2849 - 2860
[8] Essential spectrum of elliptic systems of pseudo-differential operators on L2(RN) ⊕ L2(RN)
Ibrogimov, Orif O.
Tretter, Christiane
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2017, 8 (02) : 147 - 166
[9] Lαp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\alpha }^{p}$$\end{document}-boundedness of the pseudo-differential operators associated with the Kontorovich–Lebedev transform
H. M. Srivastava
Manmohan Singh Chauhan
S. K. Upadhyay
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020, 114 (2):
[10] Essential spectrum of elliptic systems of pseudo-differential operators on L2(RN)⊕L2(RN)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2({{\mathbb {R}}}^N) \oplus L^2({{\mathbb {R}}}^N)$$\end{document}
Orif O. Ibrogimov
Christiane Tretter
Journal of Pseudo-Differential Operators and Applications, 2017, 8 (2) : 147 - 166

← 1 →