On a non-self adjoint expansion formula. (1984)

• Record Type: Journal Article
• Authors: Naylor, D.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 7:Number 3(1984)
• Page Start: 417
• Page End: 427
• Publication Date: 1984
• Subjects: integral transforms -- eigenfunction expansions -- Bessel functions; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171284000454
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : This paper develops a formula of inversion for an integral transform of the kind similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann functionY u ( k r ) and the variabler varies over the infinite intervala ≤ r < ∞ wherea > 0 The transform is useful in the investigation of functions that satisfy the Helmholtz equation and a condition of radiation at infinity. The formula established is expressed entirely in terms of series expansions and replaces earlier inversion formulas that require the evaluation of contour integrals.