Acta Mathematica Vietnamica

Submit manuscript

Online first articles

Recent issues

Volumes and issues

Volume 50
- N01
- N02
Volume 49
- N01
- N02
- N03
- N04
Volume 48
- N01
- N02
- N03
- N04
Volume 47
- N01
- N02
- N03
- N04
Volume 46
- N01
- N02
- N03
- N04
Volume 45
- N01
- N02
- N03
- N04
Volume 44
- N01
- N02
- N03
- N04
Volume 43
- N01
- N02
- N03
- N04
Volume 42
- N01
- N02
- N03
- N04
Volume 41
- N01
- N02
- N03
- N04
Volume 40
- N01
- N02
- N03
- N04
Volume 39
- N01
- N02
- N03
- N04
Volume 38
- N01
- N02
- N03
- N04
Volume 37
- N01
- N02
- N03
- N04
Volume 36
- N01
- N02
- N03
Volume 35
- N01
- N02
- N03
Volume 34
- N01
- N02
- N03
Volume 33
- N01
- N02
- N03
Volume 32
- N01
- N02&03
Volume 31
- N01
- N02
- N03
Volume 30
- N01
- N02
- N03
Volume 29
- N01
- N02
- N03
Volume 28
- N01
- N02
- N03
Volume 27
- N01
- N02
- N03
Volume 26
- N01
- N02
- N03
Volume 25
- N01
- N02
- N03
Volume 24
- N01
- N02
- N03
Volume 23
- N01
- N02
Volume 22
- N01
- N02
Volume 21
- N01
- N02
Volume 20
- N01
- N02
Volume 19
- N01
- N02
Volume 18
- N01
- N02
Volume 17
- N01
- N02
Volume 16
- N01
- N02
Volume 15
- N01
- N02
Volume 14
- N01
- N02
Volume 13
- N01
- N02
Volume 12
- N01
- N02
Volume 11
- N01
- N02
Volume 10
- N01
- N02
Volume 9
- N01
- N02
Volume 8
- N01
- N02
Volume 7
- N01
- N02
Volume 6
- N01
- N02
Volume 5
- N01
- N02
Volume 4
- N01
- N02
Volume 3
- N01
- N02
Volume 2
- N01
- N02
Volume 1
- N01
- N02

Open access issues

Generalized Convolution for the Kontorovich-Lebedev, Fourier Transforms and Applications to Acoustic Fields

Trinh Tuan , $icon-email$ Nguyen Thanh Hong , Pham Van Hoang

Abstract

To study the boundedness of the acoustic field in $L_{p} (R_{+}; d x)$ and its asymptotic behavior, we introduce a new generalized convolution for the Kontorovich-Lebedev ( $K L$ ) transform and the Fourier transforms, and a new representation of the acoustic field via this generalized convolution. Some properties of the new generalized convolution are obtained. Moreover, an analog of Watson’s theorem is established, in which we obtain the necessary and sufficient conditions for a class of generalized convolution transforms to be isomorphism-isometric.

Acta Mathematica Vietnamica

Search within journal

Generalized Convolution for the Kontorovich-Lebedev, Fourier Transforms and Applications to Acoustic Fields

Abstract