The Titchmarsh integral transformation by the index of a Bessel function

• Tipo: Artigo em Revista Científica Internacional
• Data: 2000

Autores

Yakubovich, SB (Autor) FCUP

Revista

Título: Journal of Computational and Applied Mathematics

Vol. 118

Páginas: 353-361

ISSN: 0377-0427

Editora: Elsevier

Indexação

ISI Web of Knowledge - 4 Citações

Scopus - 4 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-000-ZXH

DOI: 10.1016/s0377-0427(00)00298-3

Abstract (EN): This paper deals with an index integral transformation using Bessel functions as kernels. It was introduced and studied by Titchmarsh in 1946 as an example of a continuous spectrum Bessel-function expansions in Sturm-Liouville boundary value problems. Later in the second edition of his book (Titchmarsh, Eigenfunction Expansions Associated with Second-order Differential Equations, Part I, 2nd Edition, Clarendon Press, Oxford, 1946) in 1962 he corrected his expansion by adding an additional term, which contains a combination of an integral and series. In this paper the Titchmarsh formula is simplified and contains just integrals with Bessel and Lommel functions as kernels, which generate a pair of Titchmarsh integral transformations. By using the composition properties of the Titchmarsh transform and its relationship with the Kontorovich-Lebedev transform, L-p-properties of the Titchmarsh transform are investigated and inversion theorems are proved. The question of the correctness of Titchmarsh's formulas is completely closed by this discussion.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 9