Introduction to Pseudodifferential Operators

doi:10.1007/978-3-540-68545-6_6

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Cited by 53 publications

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The Kontorovich‐Lebedev transform and its associated pseudodifferential operator

Prasad

Mandal

2017

Math Methods in App Sciences

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In this paper, we obtained some useful estimates for convolution corresponding to Kontorovich-Lebedev transform (KL-transform) in Lebesgue space. Some continuity theorems for translation, convolution, and KL-transform in test function space H(R + ) are discussed. Then an integral representation of pseudodifferential operator involving KL-transform is found out, and its estimates in Lebesgue space is obtained. At the end, some applications of KL-transform and its convolution are discussed.

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The Kontorovich‐Lebedev transform and its associated pseudodifferential operator

Prasad

Mandal

2017

Math Methods in App Sciences

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Pseudo‐differential operator in quaternion space

Kundu

Prasad

2023

Math Methods in App Sciences

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This paper introduces the quaternion Schwarz type space, and quaternion linear canonical transform (QLCT) mapping properties are also discussed. Further, the quaternion pseudo-differential operator (QPDO) associated with QLCT is described. Some of its characteristics, including estimates, boundedness, and integral representation in quaternion Sobolev type space, are derived. Some applications of QLCT, quaternion differential equations, are also discussed.

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Pseudo-Differential Operators on the Affine Group

Dasgupta¹,

Wong²

2017

Trends in Mathematics

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Introduction to Pseudodifferential Operators

Cited by 53 publications

References 2 publications

The Kontorovich‐Lebedev transform and its associated pseudodifferential operator

The Kontorovich‐Lebedev transform and its associated pseudodifferential operator

Pseudo‐differential operator in quaternion space

Pseudo-Differential Operators on the Affine Group

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