Posted on

New PDF release: Affine density in wavelet analysis

By Gitta Kutyniok

ISBN-10: 354072916X

ISBN-13: 9783540729167

ISBN-10: 3540729496

ISBN-13: 9783540729495

In wavelet research, abnormal wavelet frames have lately come to the leading edge of present study because of questions in regards to the robustness and balance of wavelet algorithms. a huge hassle within the learn of those structures is the hugely delicate interaction among geometric homes of a chain of time-scale indices and body homes of the linked wavelet systems.

This quantity presents the 1st thorough and accomplished remedy of abnormal wavelet frames by means of introducing and using a brand new thought of affine density as a powerful software for studying the geometry of sequences of time-scale indices. a number of the effects are new and released for the 1st time. issues contain: qualitative and quantitative density stipulations for life of abnormal wavelet frames, non-existence of abnormal co-affine frames, the Nyquist phenomenon for wavelet structures, and approximation houses of abnormal wavelet frames.

Show description

Read or Download Affine density in wavelet analysis PDF

Similar functional analysis books

New PDF release: Applied Pseudoanalytic Function Theory

Pseudoanalytic functionality concept generalizes and preserves many an important positive factors of complicated analytic functionality conception. The Cauchy-Riemann procedure is changed via a way more common first-order procedure with variable coefficients which seems to be heavily concerning vital equations of mathematical physics.

An Introductory Course in Lebesgue Spaces - download pdf or read online

Introduces reader to fresh subject matters in areas of measurable functions
Includes component to difficulties on the finish of every bankruptcy ​
Content enables use with mixed-level classes
Includes non-standard functionality areas, viz. variable exponent Lebesgue areas and grand Lebesgue spaces

This e-book is dedicated solely to Lebesgue areas and their direct derived areas. special in its sole commitment, this e-book explores Lebesgue areas, distribution features and nonincreasing rearrangement. in addition, it additionally bargains with susceptible, Lorentz and the newer variable exponent and grand Lebesgue areas with massive element to the proofs. The booklet additionally touches on easy harmonic research within the aforementioned areas. An appendix is given on the finish of the ebook giving it a self-contained personality. This paintings is perfect for academics, graduate scholars and researchers.

Topics
Abstract Harmonic Analysis
Functional research

A Matlab companion to complex variables - download pdf or read online

This supplemental textual content permits teachers and scholars so as to add a MatLab content material to a posh variables path. This e-book seeks to create a bridge among capabilities of a posh variable and MatLab. -- summary: This supplemental textual content permits teachers and scholars so as to add a MatLab content material to a fancy variables direction.

Additional info for Affine density in wavelet analysis

Example text

1. Recall that the boxes Qh were chosen to be Qh = 28 3 Weighted Affine Density [e− 2 , e 2 ) × [− h2 , h2 ). Then, for h > 0 and (x, y) ∈ A, we define the boxes Qh (x, y) by h h Qh (x, y) = (x, y) Qh = {(xa, y + xb) : a ∈ [e− 2 , e 2 ), b ∈ [− h2 , h2 )} h h We remark that in this situation the sets Qh (x, y) remain rectangles, thus the geometry of the measuring boxes is easier in this sense. A left-invariant Haar measure for the group A is given by µA = dx x2 dy. Hence the volume of a box Qh (x, y) equals µA (Qh (x, y)) = µA (Qh ) = h h 2 e2 h −2 h e− 2 h h dx dy = h(e 2 − e− 2 ).

I) {Qh (ejh , khejh )}j,k∈Z is a disjoint covering of A. (ii) Any set Qrh (x, y) intersects at most jh r(eh( r+5 r+3 ) 2 −e−h( 2 ) ) h e −1 + 2(r + 2) sets of jh the form Qh (e , khe ). (iii) Any set Qrh (x, y) contains at least r(eh( r−5 r−3 ) 2 −e−h( 2 ) ) h e −1 − 2(r + 2) disjoint sets of the form Qh (ejh , khejh ). Proof. (i) Fix any (x, y) ∈ A. 3 The Notion of Affine Density by Sun and Zhou 29 ln x = jh + ln a. Further there exists a unique k ∈ Z and some b ∈ [− h2 , h2 ) such that y = ejh (kh + b).

L ∈ L2 (R), and let Λ1 , . . , ΛL ⊆ A with disL L −1 + ) < ∞. If joint union denoted by Λ = =1 Λ . Suppose that D ( =1 Λ L 2 − =1 W(ψ , Λ ) possesses a lower frame bound for L (R), then D (Λ) > 0. 6, we give a further interpretation of finite upper affine density in terms of the following definition. 3. We will say that a set K ⊆ A is affinely h-separated if (a, b) = (c, d) ∈ K =⇒ Qh (a, b) ∩ Qh (c, d) = ∅. Before proving a characterization of finite upper affine density in terms of this notion, we require the following technical lemma.

Download PDF sample

Affine density in wavelet analysis by Gitta Kutyniok


by Ronald
4.5

Rated 4.05 of 5 – based on 23 votes