The order Mehler-Fock transform and allied pseudo-differential operator

被引：0

作者：

Prasad, Akhilesh ^{[1
]}

Mandal, U. K. ^{[2
]}

Ranjan, Sudhanshu ^{[1
]}

机构：

[1] Indian Sch Mines Dhanbad, Indian Inst Technol, Dept Math & Comp, Dhanbad, India

[2] Patliputra Univ, Nalanda Coll, Dept Math, Patna, India

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2025年 / 36卷 / 03期

关键词：

Mehler-Fock transform; pseudo-differential operator; convolution; KONTOROVICH-LEBEDEV; CONVOLUTION THEOREM;

D O I：

10.1080/10652469.2024.2404049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a study related to the $ \mu <^>{th} $ mu th order Mehler-Fock transform (mu MFT) is carried out. Boundedness of translation and convolution operators in Lebesgue space are obtained. Continuity of mu MFT in Lebesgue as well as some test function spaces are discussed. Further, a pseudo-differential operator (p.d.o.) associated to mu MFT is defined and studied its continuity over certain function spaces.

引用

页码：163 / 175

页数：13

共 50 条

[21] Pseudo-differential operator associated with the fractional Fourier transform [J].

Prasad, Akhilesh ;

Kumar, Praveen .

MATHEMATICAL COMMUNICATIONS, 2016, 21 (01) :115-126

[22] Pseudo-differential operator associated with quadratic-phase Fourier transform [J].

Prasad, Akhilesh ;

Sharma, P. B. .

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2022, 28 (02)

[23] Pseudo-differential operator associated with quadratic-phase Fourier transform [J].

Akhilesh Prasad ;

P. B. Sharma .

Boletín de la Sociedad Matemática Mexicana, 2022, 28

[24] ABELIAN THEOREMS FOR DISTRIBUTIONAL KONTOROVICH-LEBEDEV AND MEHLER-FOCK TRANSFORMS OF GENERAL ORDER [J].

Gonzalez, Benito J. ;

Negrin, Emilio R. .

BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2019, 13 (03) :524-537

[25] An operational calculus for a Mehler-Fock type index transform on distributions of compact support [J].

H. M. Srivastava ;

B. J. González ;

E. R. Negrín .

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2023, 117

[26] Boundedness of Pseudo-Differential Operator Associated with Fractional Fourier Transform [J].

Prasad, Akhilesh ;

Kumar, Manish .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, 2014, 84 (04) :549-554

[27] Boundedness of pseudo-differential operator associated with fractional Hankel transform [J].

Prasad, Akhilesh ;

Singh, V. K. .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2014, 17 (01) :154-170

[28] Boundedness of pseudo-differential operator associated with fractional Hankel transform [J].

Akhilesh Prasad ;

V. K. Singh .

Fractional Calculus and Applied Analysis, 2014, 17 :154-170

[29] Boundedness of Pseudo-Differential Operator Associated with Fractional Fourier Transform [J].

Akhilesh Prasad ;

Manish Kumar .

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2014, 84 :549-554

[30] An Index Integral and Convolution Operator Related to the Kontorovich-Lebedev and Mehler-Fock Transforms [J].

Yakubovich, Semyon .

COMPLEX ANALYSIS AND OPERATOR THEORY, 2012, 6 (04) :947-970

← 1 2 3 4 5 →