Download e-book for iPad: Convolution Operators on Groups by Antoine Derighetti (auth.)

By Antoine Derighetti (auth.)

ISBN-10: 3642206557

ISBN-13: 9783642206559

This quantity is dedicated to a scientific learn of the Banach algebra of the convolution operators of a in the community compact crew. encouraged through classical Fourier research we give some thought to operators on Lp areas, arriving at an outline of those operators and Lp types of the theorems of Wiener and Kaplansky-Helson.

Show description

Read Online or Download Convolution Operators on Groups PDF

Best differential geometry books

Luther Pfahler Eisenhart's An Introduction To Differential Geometry With Use Of Tensor PDF

The various earliest books, rather these courting again to the 1900s and earlier than, at the moment are tremendous scarce and more and more dear. we're republishing those vintage works in reasonable, prime quality, glossy versions, utilizing the unique textual content and paintings.

Read e-book online Parabolic Geometries I (Mathematical Surveys and Monographs) PDF

Parabolic geometries surround a really assorted type of geometric buildings, together with such vital examples as conformal, projective, and nearly quaternionic constructions, hypersurface kind CR-structures and diverse different types of known distributions. The attribute function of parabolic geometries is an an identical description through a Cartan geometry modeled on a generalized flag manifold (the quotient of a semisimple Lie crew through a parabolic subgroup).

Joseph Grifone, Zoltan Muzsnay's Variational principles for second-order differential PDF

During this publication the writer has attempted to use "a little mind's eye and considering" to modelling dynamical phenomena from a classical atomic and molecular perspective. Nonlinearity is emphasised, as are phenomena that are elusive from the continuum mechanics viewpoint. FORTRAN programmes are supplied within the appendices An advent to formal integrability concept of partial differential structures; Frolicher-Nijenhuis concept of derivations; differential algebraic formalism of connections; helpful stipulations for variational sprays; obstructions to the integrability of the Euler-Lagrange method; the type of in the community variational sprays on two-dimensional manifolds; Euler-Lagrange platforms within the isotropic case

Additional resources for Convolution Operators on Groups

Example text

G/. p . a/Pfor every a 2 G. G/. b S / '. 6 The Fourier Transform of a Convolution Operator 21 Proof. This Theorem is a consequence of Theorem 2 and Corollary 3 of Sect. 3 and Theorem 4 of Sect. 5. b may be considered as a tempered distribution. For Remark. T b interpreted as the inverse Fourier transform of the distribution T . Corollary 2. Z/. Z/ if p 2. m/ D 2 nD 1 2 n/ dÂ; m 2 Z: 0 The following proposition gives a characterization of the Fourier transform of a p-convolution operator. Proposition 3.

G/, we have jp . G . // D G . /. T /' D T '. 18 1 Elementary Results 0 Proof. G/. Consider '1 2 '. x/j for every x 2 X and n 2 N. x/ mG 0 almost everywhere. G/. rn '1 / D 0. T /'. The following corollary improves Theorem 1. Corollary 6. G/. G/ and kT 'kp0 Ä jjjT jjjp k'kp0 . Corollary 7. G/. '/ Ä 1 : > ˇ ˇ ˇ ; G Remark. e. [63], Corollary 1, p. 12/. See also the notes to Chap. 1. G / Theorem 1 (Riesz–Thorin). X I /. Let 0 < ˛ Ä Ä 1 and let the map T W E ! G/ 19 kT 'k1=˛ Ä M1 k'k1=˛ and kT 'k1= Ä M2 k'k1= : Then T W E !

1 vn kAp D 0: Remarks. G/ has been first considered by A. Fig`aTalamanca in 1965 [44] for G abelian, for G compact but non necessarily commutative and also for G unimodular non-commutative, non-compact and p D 2. The above definition is due to Eymard [42]. G/ and kukAp D kukAp . G/ and k kA0p Ä k k. Lemma 5. Let E be a C-vector space, p a seminorm on E, F a C-subspace of E, x in the closure of F in E and " > 0. x/ C ". nD1 Proof. Let 0 < "1 < minf1; "g. G/ 37 Let y1 D v1 and yn D vn vn 1 p x for n > 2.

Download PDF sample

Convolution Operators on Groups by Antoine Derighetti (auth.)


by Thomas
4.0

Rated 4.49 of 5 – based on 24 votes