𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Paley–Wiener-Type Theorems for a Class of Integral Transforms

✍ Scribed by Vu Kim Tuan; Ahmed I. Zayed

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
176 KB
Volume
266
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

A characterization of weighted L 2 I spaces in terms of their images under various integral transformations is derived, where I is an interval (finite or infinite). This characterization is then used to derive Paley-Wiener-type theorems for these spaces. Unlike the classical Paley-Wiener theorem, our theorems use real variable techniques and do not require analytic continuation to the complex plane. The class of integral transformations considered is related to singular Sturm-Liouville boundary-value problems on a half line and on the whole line.

📜 SIMILAR VOLUMES

Weighted Lp Inequalities for a Class of
Weighted Lp Inequalities for a Class of Integral Operators Including the Classical Index Transforms
✍ Benito J. González; Emilio R. Negrin 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 74 KB

In this paper we study the behaviour of certain integral operators acting on weighted L p spaces. Particular cases include the classical integral transforms of Kontorovich and Lebedev and Mehler and Fock and the F -index transform 2 1 considered by Gonzalez, Hayek, and Negrin.

A Volterra integral type method for solv
A Volterra integral type method for solving a class of nonlinear initial-boundary value problems
✍ Bartur Jumarhon; Wilson Lamb; Sean McKee; Tao Tang 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 614 KB

It is observed that the one-dimensional heat equation with certain nonlinear boundary conditions can be reformulated as a system of coupled Volterra integral equations. A product trapezoidal scheme is proposed for the numerical solution of this integral equation system, and some numerical experiment