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Zeitschrift für Analysis und ihre Anwendungen


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Volume 25, Issue 2, 2006, pp. 193–204
DOI: 10.4171/ZAA/1284

Published online: 2006-06-30

The Plancherel and Hausdorff–Young Type Theorems for an Index Transformation

Semyon B. Yakubovich[1]

(1) Faculdade de Ciências do Porto, Portugal

The Plancherel and Hausdorff-Young type theorems are proved for an integral transformation, which is associated with the product of the modified Bessel functions of different arguments. The transform essentially generalizes Lebedev's transformation involving squares of the modified Bessel functions as kernels.

Keywords: Bessel functions, index transform, Mellin transform, Kontorovich-Lebedev transform, Plancherel theorem, Hausdorff-Young inequality, Parseval equality

Yakubovich Semyon: The Plancherel and Hausdorff–Young Type Theorems for an Index Transformation. Z. Anal. Anwend. 25 (2006), 193-204. doi: 10.4171/ZAA/1284