Subjects:  1. Applied    2. Differential Equations    3. Differential Equations - Partial Differential Equations    4. Differential equations, Parabo    5. Differential equations, Parabolic    6. Functional Analysis    7. Mathematics    8. Science/Mathematics    9. Mathematics / Functional Analysis   

Subjects:  1. Applied    2. Geometry - General    3. Mathematical Analysis    4. Mathematics    5. Reference    6. Science    7. Science/Mathematics    8. Complex analysis    9. Mathematics / Functional Analysis    10. Mathematics for scientists & engineers   

Reviews (5)

Notation...
I used this book for my first course in wavelets.Professor Frazier did a nice job bringing the material down to the undergrad by not starting off in hilbert space.He motivates it through linear algebra (for which the first chapter is an excellent review of the basics!).My only complaint is that the notation gets a bit overwhelming starting in chapter 3 (though I dont' know if I could come up with a better way to do it; just my experience).If you're looking into the subject, check out this book.It'll get you going in the right direction.

basis construction using wavelets is very well developed
Although the notation can be a little tight, the explanation of the Obscure presentation
While I don't consider myself a math expert, I have certainly had to navigate my way through undergrad level math texts on more than a few occasions. In preparation for this book, I re-read Strang's "Linear Algebra and Its Applications" (an excellent text) and felt confident that I should be able to assimilate the material from this book. From the outset, the order of presentation of material in this book seemed promising: start with a review of Linear algebra and complex numbers, continue with Discrete Fourier Transforms, and then develop discrete wavelet transforms followed by continuous wavelet transforms.Read more

Subjects:  1. Algebra - Linear    2. Algebras, Linear    3. Harmonic Analysis    4. Linear Algebra    5. Mathematical Analysis    6. Mathematics    7. Science/Mathematics    8. Wavelets (Mathematics)    9. Functional analysis    10. Mathematical theory of computation    11. Mathematics / Mathematical Analysis    12. Mathematics-Algebra - Linear    13. Wavelets   

Reviews (6)

Excellent book for people who want to actually apply special functions.
As the title indicates, the book is designed with the goal of applications front and center.That said, it is also important to note that the theoretical background is developed with full mathematical rigor.You can easily see this from the fact that whenever an infinite series is differentiated, its uniform convergence in the region of interest is always established beforehand.And this is just one example.
extremely useful, very concise
Well worth buying, extremely handy, tons of information very much organized for you

Excellent discussion of the functions used to solve PDE
Yet another excellect translation by Silverman. I've only been in possession of this book for a few days but it's already becoming a favorite mathematics text. Not a pure mathematics text but certainly a very thorough, lucid and most certainly enjoyable discussion of applied mathematics with a particularly engaging discussion of the solution of partial differential equations (Laplacian, Poisson etc.) by means of separation of variables and integral transforms. Along the way it develops the theoretical essentials of gamma functions, exponential integrals, orthogonal polynomials, Bessel functions, spherical harmonics among others. Clearly written with an emphasis on explaining the process of discovering solutions rather than merely presenting particular solutions (though it does have enlightening examples). IMO, well worth the price. ... Read more

Subjects:  1. Calculus    2. Functions, Special    3. Mathematical physics    4. Mathematics    5. Science/Mathematics    6. Functional analysis    7. Mathematics / General   

Subjects:  1. Advanced    2. Functional Analysis    3. Functions Of Real Variables    4. Mathematics    5. Science/Mathematics    6. Set Theory    7. Mathematics / Advanced    8. Real analysis   

Reviews (1)

The best function-space reference.
The study of spaces of holomorphic functions brings together techniques of complex function theory, real analysis, harmonic analysis, and functional analysis.Anyone engaged in this study should have a copy of this book, which does an excellent job of laying out the subject from all of these perspectives.The main body of the text serves as an excellent reference, and the exercises add much more.As far as this reviewer can tell, the book is cited more often in the literature than any other book on the subject.The only problem is that the book is out of print.The reviewer's (faint) hope is that this review will help convince a publisher to republish the book. ... Read more

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

Reviews (4)

Discussions are a bit convoluted.
I took Functional Analysis from professor Demkowicz.Actually the course is a misnomer, since you learn very little functional analysis and quite a bit more about set theory, Lebesgue measure theory, and topology (through Ch. 4 in the book).While I feel that the book is very meticulously written, it tries to cover in too much detail everything starting from the most basic laws of logic.The proofs and explanations are concise and clear but for my taste I also appreciate a bit of "plain English" explanation before tackling a proof, so I at least have some idea of what is going on.Only get this book if you want an *extremely* detailed development of basic theory and don't care much about applications.

Mediocre
Yet another book that resulted out of Class Notes ! Don't waste your money buying this book if you want to learn applied functional analysis. This book is meant solely for those students who have registered for Leszek's Class at UT, Austin.

A very good first book on functional analysis.
A very good first book on functional analysis. The book starts with preliminary set theory, logic, functions, and concepts of abstract algebra and moves on to the big convergence theorems in the Lebesgue integrationand onto topological and metric spaces.The book ends with basic theory ofHilbert space. Each section concludes with exercises. The author takesgreat pains to include a lot of detail in the proofs. I would recommendthis book to an advanced undergraduate or beginning graduate student. ... Read more

Subjects:  1. Algebra - General    2. Applied    3. Functional Analysis    4. Mathematical Analysis    5. Mathematics    6. Science/Mathematics    7. Mathematics / Functional Analysis   

Reviews (4)

Good introduction
I enjoyed reading this book. As another reviewer said, the proofs are a little too detailed. However, for my purposes, a little hand-holding was just what I needed. I haven't read any other books on the subject, so I can't make a thorough comparison. However, I have been reading sections of Conway's "A Course In Functional Analysis". Here are some surface differences.
A useful book, great for the beginner
This is a very self-contained book on fundamentals of functional analysis. The pace is very slow and the proofs too detailed at times. This is particularly so in Chapter 5 on Hilbert Spaces. The good thing about this book are the problems at the end of each chapter. They are mostly standard problems and a lot of 'hints' are provided (as opposed to most books in this field). I have a number of books on functional analysis but often I go back to Kubrusly's for some fundamental notion. One downside is the brief treatment on the spectral theorem for normal operators, but I guess the author's intention was too avoid using measure theoretic results, which most engineering students are not familiar with. A great pick for the engineer seeking a better understanding of higher mathematics.

Simply Indispensable
This is a must have Analisys book. Although the modest title, the book is the best introduction to functional analysis ever written. More than this, its an indispensable first book for everyone interested in operator theory. It is clear, concise and all the exercises are really solvable. You feel that the autor wants to teach you. It requires only a modest (really!) background in linear algebra and calculus. At the end, you will have learned all real analysis that so many autors (and teachers!) always have hidden from you. There are so many math disclosure in the book that I�m afraid Kubrusly being at risk of attack from any xiita math (especially the mediocre one). I agree with the last reviewer, the book is an immediate classic and Kubrusly has turned himself into a kind of Salman Rushdie for his daring in writing the Satanic Verses of the Mathematics. ... Read more

Subjects:  1. Calculus    2. Functional Analysis    3. General    4. Mathematics    5. Operator theory    6. Science/Mathematics    7. Theory Of Operators    8. Algebra    9. Mathematics / Calculus    10. Mathematics / Mathematical Analysis    11. Science-General    12. Set theory    13. Topology   

Subjects:  1. Functional Analysis    2. Geometry - Differential    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Mathematics / Mathematical Analysis    7. differential forms    8. nonlinear forms   

Subjects:  1. Functional Analysis    2. Mathematical Analysis    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Value distribution theory    7. Calculus & mathematical analysis    8. Mathematics / Number Theory    9. Mathematics and Science    10. diophantine equations    11. value distribution    12. zeta function   

Reviews (1)

FITHIS reads
Dr Ryan gave a draft of the first chapter to my supervisor Dr Sarantopoulos . He also gave me Ryan's thesis . I was fascinated because I knew only the algebraic side of the subject . The first chapter introduced me to a some aspects of functional analysis likeRademacher techniques and nuclear operators . When the book was released I hesitated to give the money . However I thought that the rest chapters would be as great . AND this TRUE . I recommend this book to everyone wanting to learn on topological tensor products ( OK , OK , Banach space tensor products) since this understanding is essential for Banach algebras and factorization in Banach spaces . I believe in retrospect that the money are not that much for the content provided . I hope Dr Ryan will publish his thesis also . To point out how good is this book I urge you to read Barry Johnsons Cohomology of Banach algebras , both give a very good picture .Also Beuazamy's book (Operator Theory) has a proof on the dulality between N(H) and B(H) . Ryans book is essential for the explanation of this phenomenon . ... Read more

Subjects:  1. Banach Spaces    2. Functional Analysis    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Tensor products    7. Topology - General    8. Transformations    9. Banach Space    10. Mathematics / Mathematical Analysis   

Subjects:  1. General    2. Geometry - General    3. Mathematics    4. Probability & Statistics - General    5. Science/Mathematics    6. Transformations    7. Banach spaces    8. Functional analysis    9. Mathematics / Differential Equations   

Reviews (2)

A Dover classic.
The spectral theorem of David Hilbert, John von Neumann, and Marshall Stone gives a complete answer to the question of which operators admit a diogonal representation, up to unitary equivalence, and makes the question precise as well. The theorem states that these are the normal operators in Hilbert space. This includes the selfadjoint operators which represent observables in quantum physics, and the more interesting ones are unbounded. Remember the Heisenberg commutation relations do not admit bounded solutions. But there is a mathematical distinction between formally selfadjoint operators (also called symmetric operators) and the selfadjoint ones. It is only the latter to which the spectral theorem applies. The distinction between the two is understood from a pair of indicies (n,m), now called deficiency indices. In some applications they represent Such an easy book to read!
This is a great intro to functional analysis. Having taken a graduate course on the subject, I used this as my text. The proofs are very readable and kept clear and simple. You'll see the subject develop before your eyes.One thing: when reading this book on infinite dimensional vector spaces,always try to draw a parallel with the finite dimensional version of thesubject, linear algebra. You'll appreciate the book all the more. For everytheorem relating to a bounded linear operator on Hilbert space, replace theoperator by a matrix on Euclidean n-space.. you'll say "oh yeah! Iremember that from linear algebra!" ... Read more

Subjects:  1. General    2. Hilbert space    3. Linear operators    4. Mathematics    5. Science/Mathematics    6. Transformations    7. Functional analysis    8. Mathematics / General    9. Science: General Issues   

Reviews (2)

Great author!
You can find the same material in a bunch of books... but the exposition by Arveson is really superb. He actually EXPLAINS things, not just a list of theorems and proofs with no apparent reason. A book to learn from.
The word "spectrum" comes from quantum theory, as does the Read more

Subjects:  1. Calculus    2. Functional Analysis    3. General    4. Mathematical Analysis    5. Mathematics    6. Science/Mathematics    7. Spectral theory (Mathematics)    8. Banach Algebra    9. C* Algebra    10. Mathematics / Mathematical Analysis    11. Spectral Ttheory   

Reviews (1)

This Book is Larger than Tolstoy's "War and Peace"
Dear Average Reader,
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Subjects:  1. Algebra    2. Algebra - Intermediate    3. Functional Analysis    4. Graphic Methods    5. Mathematics    6. Science/Mathematics    7. Theory Of Functions    8. Mathematics / General   

Reviews (1)

Great Book
This book is an excellent survey of Banach Space Theory, and an invaluable resource. It's tooterse, but then again, most reference books are. ... Read more

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

Reviews (1)

Nice guide for students and newcomers.
This book is not a textbook on harmonic analysis; it is an essay on how this important discipline has evolved and what are its main results and applications.Read more

Subjects:  1. Functional Analysis    2. Harmonic analysis    3. Infinity    4. Mathematics    5. Mathematics / Mathematical Analysis    6. Probability & Statistics - General    7. Science/Mathematics    8. Analysis    9. Calculus & mathematical analysis    10. Mathematical Analysis    11. Mathematics / Differential Equations    12. Probability & statistics   

Subjects:  1. Algebra    2. Algebra - General    3. Functional Analysis    4. Functions    5. Mathematics    6. Pre-Calculus    7. Science/Mathematics    8. Theory Of Functions    9. Mathematics / Pre-Calculus   

Subjects:  1. Differential Equations    2. Functional Analysis    3. General    4. Linear Programming    5. Mathematics    6. Science/Mathematics    7. Calculus & mathematical analysis    8. Mathematics / General   

Reviews (10)

A solid introduction to level sets
I read this book and Sethian's book and found this one to be much easier to read.The presentation follows a logical sequence and looks much less like someone's thesis than Sethian's text.Level sets and many of their various applications are covered in relative detail for a book of this size.
Solid introduction intended for numerical PDE people
This book provides a good introduction (and extensive references) to the level set method.The major implementation details are given (with the finite difference formulas).The book is intended for people who already know something about numerical PDE's and CFD (computational fluid dynamics).Not all of the details are given (such as smoothing of the level set when computing curvature), but this will probably be addressed in a future volume.Overall, this book will get you started with actual computations.But do not be afraid to consult the more recent literature on the subject.

A Bad Way To Learn Level Set Methods
If you're new to level set methods and are hoping to learn to implement them computationally, this is the WRONG book for you.This book reads like a 250 page review paper.Most of the material it covers is explained in much better detail in the references it provides.
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Subjects:  1. Advanced    2. Analytic Mechanics (Mathematical Aspects)    3. Calculus    4. Functional Analysis    5. General    6. Implicit functions    7. Level set methods    8. Mathematical Physics    9. Mathematics    10. Number Systems    11. Science/Mathematics    12. Analytical mechanics    13. Applied mathematics    14. Mathematics / Number Systems    15. Theoretical methods