Abstract Harmonic Analysis of Continuous Wavelet Transforms - download pdf or read online

By Hartmut Führ

ISBN-10: 3540242597

ISBN-13: 9783540242598

This quantity includes a systematic dialogue of wavelet-type inversion formulae according to staff representations, and their shut connection to the Plancherel formulation for in the neighborhood compact teams. the relationship is verified through the dialogue of a toy instance, after which hired for 2 reasons: Mathematically, it serves as a robust device, yielding lifestyles effects and standards for inversion formulae which generalize a number of the identified effects. in addition, the relationship presents the start line for a – quite self-contained – exposition of Plancherel conception. as a result, the publication is additionally learn as a problem-driven creation to the Plancherel formula.

Show description

Read Online or Download Abstract Harmonic Analysis of Continuous Wavelet Transforms PDF

Similar mathematical analysis books

Download PDF by Zhilin Li: The Immersed Interface Method: Numerical Solutions of PDEs

Interface difficulties come up whilst there are various fabrics, reminiscent of water and oil, or an analogous fabric at various states, resembling water and ice. If partial or traditional differential equations are used to version those functions, the parameters within the governing equations tend to be discontinuous around the interface keeping apart the 2 fabrics or states, and the resource phrases are frequently singular to reflect source/sink distributions alongside codimensional interfaces.

Statistics of Random Processes: I. General Theory by Robert S. Liptser, Albert N. Shiryaev, B. Aries PDF

The topic of those volumes is non-linear filtering (prediction and smoothing) concept and its program to the matter of optimum estimation, keep watch over with incomplete info, info conception, and sequential checking out of speculation. the necessary mathematical heritage is gifted within the first quantity: the idea of martingales, stochastic differential equations, absolutely the continuity of likelihood measures for diffusion and Ito approaches, parts of stochastic calculus for counting tactics.

Download e-book for kindle: An Introduction to Fourier Analysis and Generalised by M. J. Lighthill

This monograph on generalised capabilities, Fourier integrals and Fourier sequence is meant for readers who, whereas accepting concept the place every one element is proved is best than one in line with conjecture, however search a therapy as trouble-free and unfastened from problems as attainable. Little distinct wisdom of specific mathematical innovations is needed; the booklet is appropriate for complicated college scholars, and will be used because the foundation of a quick undergraduate lecture direction.

Extra info for Abstract Harmonic Analysis of Continuous Wavelet Transforms

Example text

Suppose that f ∈ L2 (G). (a) Vf : L2 (G) → L2 (G) is a closed operator with domain dom(Vf ) = {g ∈ L2 (G) : g ∗ f ∗ ∈ L2 (G)} , and acts by Vf g = g ∗ f ∗ . The subspace dom(Vf ) is invariant under left translations. (b) If f ∆−1/2 ∈ L1 (G), then f is a bounded vector, with Vf ≤ f ∆−1/2 1 . This holds in particular when f has compact support. (c) If f ∗ ∈ L2 (G) then L1 (G) ∩ L2 (G) ⊂ dom(Vf ). (d) Suppose that f ∗ ∈ L2 (G). Then Vf∗ ⊂ Vf ∗ . If one of the operators is bounded, so is the other, and they coincide.

25) Proof. 23. 25(c), Cπi ηi = 1 is the admissibility condition on ηi . 15) shows that whenever πi πj , Im(Vηi )⊥Im(Vηi ) ⇐⇒ Cπj Si,j ηi , Cπj ηj = 0 . 24 yields Im(Vηi )⊥Im(Vηi ) for arbitrary vectors ηi and ηj , whenever πi πj . Hence the proof is finished. 22. Here we only consider the case of direct sums of discrete series representations. Some of the phenomena encountered in the general case can be already examined in this simpler setting, in particular the striking difference between unimodular and nonunimodular groups and the role of the formal dimension operators in this context.

Let S ∈ L2 (G) be a selfadjoint convolution idempotent, then for all f ∈ H = L2 (G) ∗ S we have f ∞ ≤ f 2 S 2 . Proof. This follows from the Cauchy-Schwarz inequality: |f (x)| = |(f ∗ S ∗ )(x)| = | f, λG (x)S | ≤ f 2 S 2 . The following proposition gives rise to a somewhat subtle distinction between unimodular and nonunimodular groups: In the unimodular case, any invariant subspace of L2 (G) which has admissible vectors possesses one in the form of a convolution idempotent. 43 below. 40. Suppose that H ⊂ L2 (G) is closed and leftinvariant.

Download PDF sample

Abstract Harmonic Analysis of Continuous Wavelet Transforms by Hartmut Führ


by Brian
4.5

Rated 4.76 of 5 – based on 26 votes

About admin