Beurling's theorems and inversion formulas for certain index transforms

• Autorzy: Yakubovich S. B.
• Języki publikacji: EN

Abstrakty

EN

The familiar Beurling theorem (an uncertainty principle), which is known for the Fourier transform pairs, has recently been proved by the author for the Kontorovich-Lebedev transform. In this paper analogs of the Beurling theorem are established for certain index transforms with respect to a parameter of the modified Bessel functions. In particular, we treat the generalized Lebedev-Skalskaya transforms, the Lebedev type transforms involving products of the Alacdoriald functions of different arguments and an index transform with the Nicholson kernel function. We also find inversion formulas for the Lebedev-Skalskaya operators of an arbitrary index and the Nicholson kernel transform.

Słowa kluczowe

EN

Beurling theorem; Kontorovich-Lebedev transform; Lebedev-Skalskaya transforms; Fourier transform; Laplace transform; modified Bessel functions; uncertainty principle; Nicholson function

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 1
• Strony: 93--110
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Yakubovich S. B.

• University of Porto, Faculty of Sciences, Department of Pure Mathematics, Campo Alegre st., 687, 4169-007 Porto, Portugal,

Bibliografia

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• [14] S.B. Yakubovich, The Planchcrel and Hausdorff-Young type theorems for an index transformation, Journal for Analysis and its Applications 25 (2006), 193-204.
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• [16] S.B. Yakubovich, A class of integral equations and index transformations related to the modified and incomplete Bessel functions. Preprint. CMUP. 2008, 19 pp.