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Completeness and basis properties of...

Higgins, J. R. (1935-)

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Completeness and basis properties of sets of special functions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Completeness and basis properties of sets of special functions/ J.R. Higgins.
remainder title:	Completeness & Basis Properties of Sets of Special Functions
Author:	Higgins, J. R.
Published:	Cambridge :Cambridge University Press, : 1977.,
Description:	x, 134 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Functions, Special. -
Online resource:	https://doi.org/10.1017/CBO9780511566189
ISBN:	9780511566189

Completeness and basis properties of sets of special functions
Higgins, J. R.1935-

Completeness and basis properties of sets of special functions[electronic resource] /Completeness & Basis Properties of Sets of Special FunctionsJ.R. Higgins. - Cambridge :Cambridge University Press,1977. - x, 134 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;72. - Cambridge tracts in mathematics ;72..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

This tract presents an exposition of methods for testing sets of special functions for completeness and basis properties, mostly in L2 and L2 spaces. The first chapter contains the theoretical background to the subject, largely in a general Hilbert space setting, and theorems in which the structure of Hilbert space is revealed by properties of its bases are dealt with. Later parts of the book deal with methods: for example, the Vitali criterion, together with its generalisations and applications, is discussed in some detail, and there is an introduction to the theory of stability of bases. The last chapter deals with complete sets as eigenfunctions of differential and a table of a wide variety of bases and complete sets of special functions. Dr Higgins' account will be useful to graduate students of mathematics and professional mathematicians, especially Banach spaces. The emphasis on methods of testing and their applications will also interest scientists and engineers engaged in fields such as the sampling theory of signals in electrical engineering and boundary value problems in mathematical physics.

ISBN: 9780511566189Subjects--Topical Terms:

606076
Functions, Special.

LC Class. No.: QA351 / .H57 1977

Dewey Class. No.: 515.5

Completeness and basis properties of sets of special functions
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100 1 $a Higgins, J. R. $q (John Rowland), $d 1935- $3 3470516
245 1 0 $a Completeness and basis properties of sets of special functions $h [electronic resource] / $c J.R. Higgins.
246 3 $a Completeness & Basis Properties of Sets of Special Functions
260 $a Cambridge : $b Cambridge University Press, $c 1977.
300 $a x, 134 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 72
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
520 $a This tract presents an exposition of methods for testing sets of special functions for completeness and basis properties, mostly in L2 and L2 spaces. The first chapter contains the theoretical background to the subject, largely in a general Hilbert space setting, and theorems in which the structure of Hilbert space is revealed by properties of its bases are dealt with. Later parts of the book deal with methods: for example, the Vitali criterion, together with its generalisations and applications, is discussed in some detail, and there is an introduction to the theory of stability of bases. The last chapter deals with complete sets as eigenfunctions of differential and a table of a wide variety of bases and complete sets of special functions. Dr Higgins' account will be useful to graduate students of mathematics and professional mathematicians, especially Banach spaces. The emphasis on methods of testing and their applications will also interest scientists and engineers engaged in fields such as the sampling theory of signals in electrical engineering and boundary value problems in mathematical physics.
650 0 $a Functions, Special. $3 606076
650 0 $a Series, Orthogonal. $3 752179
650 0 $a Lp spaces. $3 620345
830 0 $a Cambridge tracts in mathematics ; $v 72. $3 3470517
856 4 0 $u https://doi.org/10.1017/CBO9780511566189