Introduction to Hilbert Spaces with Applications 3rd Edition by Lokenath Debnath (PDF)

Description

Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory.Updated chapter on waveletsImproved presentation on results and proofRevised examples and updated applicationsCompletely updated list of references

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Personally, I consider this a great book to read. It’s a joy to read all the time.This book explains each subject very well. I like the Chapters on Lebesgue Measure and Integration Theory, Hilbert Spaces and Linear Operators. I rated 5 stars because this book has very clear proofs of every theorem it presents.The authors are well-known professors and mathematicians, and they produce synergy when they work together. I have both editions (old and new), because the new one have better presentation in most of the chapters, and it has new chapters also.I love this book! That’s it!I highly recommend this book to any one interested in the subject of Functional Analysis.

⭐this is a very good book it describes and explains very difficult concepts like the lebesgue integral in a very user friendly way.

⭐Nearly brand new book

⭐Clearest introduction I know to inner-product spaces.

⭐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.This book by Debnath, is a good example of a book fitting the above criteria. It is an excellent book for self-study of Hilbert spaces, Fourier Transforms and other subjects in Functional Analysis. I found it to be a useful supplement to Folland’s “Real Analysis” which I used as a 1st-year graduate student in mathematics. In fact, this book saved me a few times, when I had to figure out solutions to difficult homework excercises. One example comes to mind is a homework assignment (I think that it was out of Folland’s book) involving Rademacher and Walsh functions, which are covered in this book. I also found this text for useful in studying for my candidacy examination.In summary, this book is would make an excellent addition to your library. (If you are also interested in the subject of elliptic functions, then “Elliptic and Associated Functions with Applications” by Debnath and M. Dutta (World Press Private Ltd., Calcutta, 1965), may interest you. It is, like the above text, excellent, but very difficult to find!)

⭐There is a spot on certain page but generally the book is really good

⭐bardcover, good, but may be the package could be better.

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