Reviews (4)

The creation of an ethos
A comprehensive exposition of the Sobolev creation: the ethos of the solutions for differential equations. Ethos means dwelling, but much more than abode it means a way of being. The Sobolev spaces are the whole being of the solutions, the way they are. The way they look like.
An invaluable resource
As a PhD student in mathematics focusing on theoretical PDE, I find this monograph to be one of the most useful in my collect. The book is self contained and very easy to read, requiring only a background in real analysis at the beginning graduate/senior undergrad level. This text covers a wide range of topics from the basics of topological vector spaces, all the way through interpolation methods and Besov spaces, but maintains a deep enough level so that most researchers will find this book to be very useful as a reference for the subject. In particular, I really like the completeness by which the imbedding theorems in the book are stated and proved. In addition to the content, the book is also beautifully bound and is printed on very high quality paper.

very interesting
A very interesting textbook for people interested in functional analysis. It provides a great introduction for beginners but also clear and rigorous demonstrations of more technical points. ... Read more

Subjects:  1. Applied    2. Differential Equations    3. Mathematics    4. Science/Mathematics    5. Functional analysis    6. Mathematics / Statistics   

Reviews (1)

From Fourier to wavelets to applications.
I take it as a healthy sign when there is a burst of new books in a sub-area of math. In wavelet analysis and its applications, we have seen a number of recent books arrive to university bookstores. Surprisingly there doesn't in fact seem to be much of an overlap of subject or scope, from one book to the next. The subject is infinite in many directions, for example the kind of student it is aimed at, the level, the specialized area within math itself, and the kind of application it is stressing. D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material, for example Fourier series, than is typically the case in a graduate text. It goes from Haar systems to multirelutions, and then the discrete wavelet transform, starting on page 215. The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes.-- Highly recommended! ... Read more

Subjects:  1. Applied    2. Functional Analysis    3. Harmonic Analysis    4. Mathematical Analysis    5. Mathematics    6. Science/Mathematics    7. Wavelets (Mathematics)    8. Fourier Analysis    9. Mathematics / Applied    10. Sound, vibration & waves (acoustics)    11. Wavelets   

Reviews (2)

An Immediate Classic
This book is an essential tool for anyone working in long awaited mathematical introduction to time-frequency
This book fills a long-standing gap in the literature. While Gabor analysis is described on equal footing with wavelets in the early literature on the subject (in the late 80's) the book market on wavelets exploded, while no "serious" (from a mathematician's point of view) introduction to Gabor analysis was available. Maybe the impossibility of having orthonormal Gabor bases was the main reason for this situation (by the Balian-Low theorem).In 13 Chapters the author takes the reader from basic Fourier analysis and fundamental facts concerning the short-time Fourier transform and uncertainty to the foundations of Gabor analysis, i.e. Gabor frames, the structure of the Gabor frame operator, Zak transform methods, the role of the Heisenberg group and to functional analytic results describing the "appropriate" function spaces (so-called modulation spaces), playing here the same role as Besov spaces play with respect to wavelet expansions. Besides summarizing known results and proving things from scratch interesting applications (e.g. to pseudo- differential operators) are provided. The book should be of great interest to mathematicians (e.g. graduate students in analysis) as well as those applied scientist who want to read about the "foundations" of this field without having to consult dozends of original papers. A great book which will have its influence on the teaching of the subject in the years to come. ... Read more

Subjects:  1. Applied    2. Engineering - Electrical & Electronic    3. Frequency spectra    4. Functional Analysis    5. Mathematics    6. Probability & Statistics - General    7. Science/Mathematics    8. Signal Processing (Communication Engineering)    9. Signal processing    10. Technology    11. Telecommunications    12. Time Series Analysis    13. Time-series analysis    14. Fourier analysis    15. Probability & statistics    16. Sound, vibration & waves (acoustics)    17. Technology / Engineering / Electrical    18. analysis    19. wavelets   

Reviews (2)

The standard work, but there are better
This is the "standard" book on the subject. It is referenced everywhere. It has a lot in it. I have not read it cover to cover, just used it for reference, but if you are new to the subject I think Kolmogorov and Fomin looks beeter, and Shilov's books look better too.

Very readable classic
This book is a bargain ... in these days of $100 paperbacks ! The foreign authors, who 1st published this in the early 50s, write in a very readable way as opposed to most US profs. The book starts with an example of a continuous function which is not differentiable and then proves Lebesgue's theorem which tells you when a function does have a derivative.The 2nd part of the book is about Integral equations which again starts with some examples of problems the early 19th century mathematicians solved. Particularly interesting to me was Fredholm's method which was to replace the integral with a series. The book covers all the topics you would expect in a very readable form. ... Read more

Subjects:  1. Calculus    2. Functional analysis    3. Mathematics    4. Science/Mathematics    5. Mathematics / General   

Reviews (4)

advanced coverage
This is an advanced treatment of prime numbers. But it is not all abstract number theory. The recurrent theme is how to compute these and how to use primes in other computationally intensive tasks.
Badly Bound
The book content is quite fascinating; the only real readability difficuly is some rather obscure and undefined notation. Standard reference on the subject.
While recently published, this book is shaping to become the standard reference on the theory that surrounds prime numbers in a computational setting, drawing from all branches of number theory, as well as abstract algebra, analysis, combinatorics, statistics, complexity theory and elliptic curves. Surely a multidisciplinary treatise if there ever was one.Read more

Subjects:  1. Functional Analysis    2. Mathematics    3. Number Theory    4. Numbers, Prime    5. Science/Mathematics    6. Mathematics / Number Theory   

Subjects:  1. Calculus    2. Calculus, Operational    3. Differential Equations    4. Functional Analysis    5. Mathematics    6. Science/Mathematics    7. Theory of distributions (Functional analysis)    8. Transformations (Mathematics)    9. Mathematics / Functional Analysis   

Reviews (3)

Helpful for math majors only
I've used this book during my differential class over the last semester.The problems in the book are carried out well and the back of the book has even and odd answers to help your understanding.For math majors, this book is great because it really wants you to "experience" the world of diff EQ, but for engineers or others taking it as a side class, it doesn't offer good examples for getting the job done.A good instructer can correct this though.As a book, 3 stars.

Very good
Fast and its just brand new, he never opened the books

Good book but a strong background on calculus required.
This book will tell you everything you need to learn on differentialequations.It covers thoroughly the methods for solving first and secondorder differential equations.The book also extends into Fouriertransforms.I used this book at MIT for the differential equations classand found it very useful. Within its contents, matlab exercises are presentand some simple projects which lets the student apply its knowledge. Theonly problem with the book is that it can be hard to read at certainpoints.Also the author assumes a strong background in calculus. ... Read more

Subjects:  1. Boundary Value Problems    2. Differential Equations    3. Functional Analysis    4. Mathematics    5. Science/Mathematics    6. Mathematics for scientists & engineers   

Subjects:  1. Applied    2. Calculus    3. Convex functions    4. Convex sets    5. Functional Analysis    6. Functions Of Real Variables    7. Linear Programming    8. Mathematical Analysis    9. Mathematics    10. Science/Mathematics    11. Calculus & mathematical analysis    12. Convex analysis    13. Mathematical theory of computation    14. Mathematics / Linear Programming    15. mathematical programming    16. nondifferentiable optimization    17. nonsmooth optimization    18. numerical algorithms   

Reviews (2)

Buy this book!
if you want to learn tensor analysis in clear language, this book is for you ! fantastic introduction to the subject. The exposition is quite clear ! BUY IT!

Tensor analysis for all
This is a well-written and careful introduction to theRead more

Subjects:  1. Calculus of tensors    2. Engineering - Civil    3. Engineering - Mechanical    4. Functional Analysis    5. Mathematics    6. Science/Mathematics    7. Vector & tensor analysis   

Reviews (2)

superb introduction to Functional analysis
Daya Reddy has produced a new edition of an older text which now has someextra material and has improved the explanations of the earlier edition aswell as include many useful diagrams.This is an excellent introduction toFunctional Analysis avoiding the often seen theorem/proof approach whichoverwhelms students who are not literate in the mathematics. All conceptsare very well explained and demonstrated, the progression is slow andcareful so as not to disallusion students who are not pure mathematicians.Even for mathematicians this is a good, gentle introduction. When I firstsaw the earlier edition in the library I was captivated by the style andease of development so I emailed Professor Reddy and asked about a newedition, the preprint of which he sent me to peruse, I then later boughtthe new one as it came out. The beauty and power of functional analysis isalso evident The most readablefunctional analysis book for engineers.
This book is essentially the second edition of his now out of print book titled "Functional Analysis and Boundary-Value Problems: An Introductory Treatment". I like this bood very much. It is not verydemanding on mathematical procedures, but lays out the nessary concepts ina very logical progression for Engineers and none math majors, though somemath people may not like it. The examples and graphs are very revealing;they illustrates mathematical concepts very well, makes them easier tounderstand. Read more

Subjects:  1. Calculus    2. Finite Element Method (Mathematics)    3. Functional Analysis    4. Mathematical Analysis    5. Mathematics    6. Science/Mathematics    7. Mathematics / Functional Analysis    8. Mathematics / Mathematical Analysis    9. Mathematics-Calculus    10. Numerical analysis   

Subjects:  1. Calculus    2. Functional Analysis    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Mathematics / Functional Analysis    7. Mathematics / Mathematical Analysis    8. Mathematics-Calculus    9. Mathematics-Mathematical Analysis   

Subjects:  1. Calculus    2. Functional Analysis    3. General    4. Mathematical Analysis    5. Mathematics    6. Problems, exercises, etc    7. Science/Mathematics    8. Mathematics / Calculus    9. Mathematics / Functional Analysis    10. Mathematics-Functional Analysis    11. Mathematics-Mathematical Analysis   

Subjects:  1. Algebra - Linear    2. Differential Equations    3. Harmonic analysis    4. Homogeneous spaces    5. Lie groups    6. Mathematics    7. Number Theory    8. Science/Mathematics    9. Fourier transfoms    10. Functional analysis    11. Mathematics / Mathematical Analysis    12. several complex variables   

Reviews (3)

Very good book
Lokenath Debnath, like many authors from India, I am finding, write solid mathematical texts.These texts tend to be well-organized, clear, and do not leave out or fail to emphasize important concepts.The proofs are easy to understand.It does not take a week just to read a few pages. Good book to teach yourself this interesting subject
I'm a statistician who has been using Part 1 of this book to teach myself the basics of Hilbert space theory. So far, I've been very pleased with it. Great and Clear
Debhath and Mikusinski used great and clear Mathematics and diagrams to explain the theory and applications. I especially like chapter seven "Mathematical Foundations of Quantum Mechanics" and chapter eight"Wavelet". This book is suitable for graduate engineeringstudents. ... Read more

Subjects:  1. Advanced    2. Applied    3. Hilbert space    4. Mathematics    5. Science/Mathematics    6. Set Theory    7. Functional analysis    8. Mathematics / Advanced   

Subjects:  1. Boundary value problems    2. Differential Equations    3. Fourier series    4. Functional Analysis    5. Functions, Orthogonal    6. Infinity    7. Mathematics    8. Science/Mathematics    9. Mathematics / Differential Equations   

Subjects:  1. Calculus    2. Functional Analysis    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Mathematics / Mathematical Analysis   

Subjects:  1. Functional Analysis    2. Mathematics    3. Number Theory    4. Probability & Statistics - General    5. Science/Mathematics    6. Complex analysis    7. Mathematics / Number Theory    8. Probability & statistics   

Reviews (8)

Caveat
This is a great book for understanding the specifics of implementation of wavelet transforms and lifting schemes. One warning, however, the book is rife with errors and the reader would be well-advised to check calculations.

very good book fills a missing hole in wavelet literature
Just picked up a copy of this book.
A must read for Lifting Based Wavelet Transforms
You always wondered, what is "Lifting" with respect to wavelets. Well you have this book..and I must say, this will definately solve all your doubts abt Lifting. I use this book, and recommend it to anyone, who wish to explore the wonderful world of wavelet based transforms. An in-depth analysis of multi-rate transforms, Laurent polynomial division and actual MATLAB-based exmaples enhance the beauty of this book. Amongst the vast majority of books out there, Check out this one ! ... Read more

Subjects:  1. Engineering - Electrical & Electronic    2. Functional Analysis    3. Harmonic Analysis    4. Mathematical Analysis    5. Mathematics    6. Science/Mathematics    7. Signal Processing (Communication Engineering)    8. Wavelets (Mathematics)    9. Calculus & mathematical analysis    10. Lifting    11. Mathematics / Mathematical Analysis    12. Mathematics for scientists & engineers    13. Wavelets    14. signal processing    15. time-frequency analysis    16. wavelett packets   

Subjects:  1. Differential Equations    2. Functional Analysis    3. General    4. Global Analysis    5. Mathematics    6. Numerical Analysis    7. Probability & Statistics - General    8. Science/Mathematics    9. Hamiltonian and reversible systems    10. Mathematics / Differential Equations    11. Mathematics / Number Systems    12. Mathematics for scientists & engineers    13. Medical-General    14. Numerical solutions    15. differential equations on manifolds    16. geometric numerical integration    17. symplectic and symmetric methods   

Reviews (8)

The best book for Fourier transform
When I came to the field of Fourier transform, the book provides me a clear, easy-understanding picture to the field so that I believe any of you can get into the field by use of the book. If you are looking for your first book to Fourier transform, don't waste your time, it is. Even through my life in the research, I depended on it most of the time. It's too great.

Good book on practical, fourier analysis, excellent problems
This book is an old classic in fourier analysis - it emphasizes intuitive understanding and uses images a lot to convey information, e.g. the book includes a pictorial dictionary of fourier transforms, and recommends using the method of dragging a strip of paper to get a better understanding of convolutions. The problems are challenging and very interesting, e.g. one problem asks the reader to explain the differences in spectra when reconstructing a signal by linear interpolation vs. sketching a smooth graph between the sample points by hand. (there are also easier problems for to begin with, before one tackles "engineering" questions as the one above)Highly recommended!

excellent on fundamentals
If you are looking for thorough explanations with great physical insight - this is the book to get. It is for people who want to know WHY more than HOW. However, If you are looking for how (to implement), I suggest the book"Fast Fourier Transform" by Brigham ... Read more

Subjects:  1. Applied    2. Engineering - Electrical & Electronic    3. Fourier Analysis    4. Fourier transformations    5. Harmonic Analysis    6. Mathematical Analysis    7. Mathematics    8. Science/Mathematics    9. Technology & Industrial Arts    10. Transformations (Mathematics)    11. Functional analysis    12. Medical physics    13. Optics (light)    14. Sound, vibration & waves (acoustics)    15. Technology / Engineering / Electrical