Convergence Results for an Extension of the Fourier Transform

Carlo Belingeri and Paolo Emilio Ricci
Additional contact information
Carlo Belingeri: Università degli Studi di Roma “La Sapienza”, Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
Paolo Emilio Ricci: Università degli Studi di Roma “La Sapienza”, Dipartimento di Matematica “Guido Castelnuovo”

A chapter in Approximation, Probability, and Related Fields, 1994, pp 119-126 from Springer

Abstract: Abstract In a preceding paper (see2), for any function f such that: $${x^k}f\left( x \right) \in L\left( {a,b} \right),\forall k \in \mathbb{N} \cup \left\{ 0 \right\},$$ , we have considered the integral transform: 1.1 $$ \hat f\left( y \right): = \int\limits_a^b {F\left( {x,y} \right)f\left( x \right)} dx, $$ related to the kernel F(x,y) which is the generating function of a set of polynomials orthogonal in (a,b) with respect to the weight W(x) (shortly O.P.S.). We have proved that the integral transforms of this kind can be considered in some sense as a generalization of the Fourier transform, since they formally verify a property which is analogous to a known property of this classical operator.

Date: 1994
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-2494-6_8

Ordering information: This item can be ordered from
http://www.springer.com/9781461524946

DOI: 10.1007/978-1-4615-2494-6_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().