Lecture Notes in Mathematics

By: Gitta Kutyniok

Write A Review

Paperback | 12 July 2007

At a Glance

Paperback
156 Pages

Dimensions(cm)
23.5 x 15.88 x 0.64

Paperback

$59.99

or 4 interest-free payments of $15.00 with

Ships in 5 to 7 business days

In wavelet analysis, irregular wavelet frames have recently come to the forefront of current research due to questions concerning the robustness and stability of wavelet algorithms. A major difficulty in the study of these systems is the highly sensitive interplay between geometric properties of a sequence of time-scale indices and frame properties of the associated wavelet systems.

This volume provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Many of the results are new and published for the first time. Topics include: qualitative and quantitative density conditions for existence of irregular wavelet frames, non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Geometry Computing & I.T.Computer Science Mathematical Theory of Computation

Introduction	p. 1
Irregular Wavelet and Gabor Frames	p. 1
Density for Gabor Systems	p. 3
Geometry of Time-Scale Indices	p. 5
Overview of Main Results	p. 7
Wavelet and Gabor Frames	p. 11
Frame Theory	p. 11
Wavelet Analysis	p. 13
Time-Frequency Analysis	p. 16
Amalgam Spaces	p. 19
Weighted Affine Density	p. 21
Definitions	p. 21
Basic Properties	p. 24
The Notion of Affine Density by Sun and Zhou	p. 27
Comparison of Both Notions of Affine Density	p. 32
Qualitative Density Conditions	p. 35
Existence of an Upper Frame Bound	p. 35
Existence of a Lower Frame Bound	p. 37
Examples of Wavelet Systems	p. 42
Density of Sequences in R+	p. 45
Affine Density and the Local Integrability Condition	p. 48
Amalgam Spaces on R {0}	p. 48
A Density Version of the Local Integrability Condition	p. 50
A Characterization of Wavelet Parseval Frames	p. 56
Quantitative Density Conditions	p. 59
Outline and Comparison with Previous Work	p. 59
Density of Product Sequences	p. 61
A Fundamental Relationship	p. 63
The Nyquist Phenomenon	p. 75
Sufficient Density Conditions for Wavelet Frames	p. 76
Existence of Special Weight Functions	p. 81
Co-Affine Systems	p. 82
Homogeneous Approximation Property	p. 87
Amalgam Spaces and the Continuous Wavelet Transform	p. 87
The Basic Class B[subscript 0]	p. 89
The Homogeneous Approximation Property for Wavelet Frames	p. 93
The Comparison Theorem for Wavelet Frames	p. 97
Density Results for Wavelet Schauder Bases	p. 100
Weighted Beurling Density and Shift-Invariant Gabor Systems	p. 105
Motivation and Outline of Chapter	p. 105
Weighted Beurling Density	p. 107
Littlewood-Paley Type Inequalities	p. 110
Equivalent Definition of Weighted Beurling Density	p. 115
Beurling Density, Frame Bounds, and Gabor Generators	p. 119
Shift-Invariant Gabor Systems	p. 121
References	p. 127
Index	p. 135
Table of Contents provided by Ingram. All Rights Reserved.

Lecture Notes in Mathematics

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Mathematical Theory of Computation

AI Engineering

Building Applications with Foundation Models

Algorithms in C, Parts 1-4

3rd Edition - Fundamentals, Data Structures, Sorting, Searching

Discrete Mathematics for Computing

Grassroots

Swim Training Patterns

1st Edition - Plan your Training Sessions with the Power of Mathematics

The Delicate Art of Brute Force

How to Compute It When You Can't Solve It

Effective Machine Learning Teams

Best Practices for ML Practitioners

Nonlinear Analysis for Human Movement Variability

AI for Decision Intelligence in Critical Systems

Advances in Applied Mathematics

AI for Decision Intelligence in Critical Systems

Advances in Applied Mathematics

Mathematical Foundations of Deep Learning

Theory and Algorithms

Mathematical Foundations of Deep Learning

Theory and Algorithms

Decentralized Futures

Navigating the Integration of Blockchain Technology with Artificial Intelligence

Theory of Computation for Software Developers

Theory of Computation for Software Developers

AI and Blockchain in Smart Grids

Fundamentals, Methods, and Applications

Attack-and-Defense Games for Control Systems

Analysis and Synthesis

Introduction to Modern Cryptography

Revised Third Edition

Machine Learning Interviews

Kickstart Your Machine Learning and Data Career

Zhang Time Discretization (ZTD) Formulas and Applications

Computability and Computational Explanation

Elements in the Philosophy of Mathematics

Computability and Computational Explanation

Elements in the Philosophy of Mathematics

Machine Learning Pocket Reference

Working with Structured Data in Python

Ten Software Patterns Every Student Should Know

Distributed Computer and Communication Networks

28th International Conference, DCCN 2025, Moscow, Russia, September 22-26, 2025, Revised Selected Papers

This product is categorised by