The distribution of the eigenvalues of differential operators has long fascinated mathematicians. Recent advances have shed new light on classical problems in this area, and this book presents a fresh approach, largely based on the results of the authors. The emphasis here is on a topic of central importance in analysis, namely the relationship between i) function spaces on Euclidean n-space and on domains; ii) entropy numbers in quasi-Banach spaces; and iii) the distribution of the eigenvalues of degenerate elliptic (pseudo) differential operators. The treatment is largely self-contained and accessible to nonspecialists.
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Editorial Reviews
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"The book is an excellent introduction....The basic ideas are well outlined and supported by complete proofs." Georgi E. Karadzhov, Mathematical Reviews
Book Description
The distribution of the eigenvalues of differential operators has long fascinated mathematicians. Recent advances have shed new light upon classical problems in this area, and this book presents a fresh approach, largely based upon the results of the authors. The emphasis here is on a topic of central importance in analysis, namely the relationship between i) function spaces on Euclidean n-space and on domains; ii) entropy numbers in quasi-Banach spaces; and iii) the distribution of the eigenvalues of degenerate elliptic (pseudo) differential operators. The treatment is largely self contained and accessible to non-specialists. Both experts and newcomers alike will welcome this unique exposition.
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Inside This Book
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First Sentence:
This chapter is devoted to the general functional-analytic preliminaries which will be needed throughout the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
spaces bpq, regular elliptic differential operator, degenerate pseudodifferential operators, kth approximation number, smoothness theory, weighted function spaces, limiting embeddings, notational agreement, dyadic resolution, localisation principle, entropy numbers, degenerate elliptic operators, complex interpolation method, compact embeddings, embedding constants, negative spectrum, weighted spaces, atomic representations, usual modification, approximation numbers, admissible representations, unweighted case, eigenvalue distributions, algebraic multiplicity, root spaces Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proof Step, Proposition Let, Theorem Suppose, Proof Let New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter is devoted to the general functional-analytic preliminaries which will be needed throughout the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
spaces bpq, regular elliptic differential operator, degenerate pseudodifferential operators, kth approximation number, smoothness theory, weighted function spaces, limiting embeddings, notational agreement, dyadic resolution, localisation principle, entropy numbers, degenerate elliptic operators, complex interpolation method, compact embeddings, embedding constants, negative spectrum, weighted spaces, atomic representations, usual modification, approximation numbers, admissible representations, unweighted case, eigenvalue distributions, algebraic multiplicity, root spaces Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proof Step, Proposition Let, Theorem Suppose, Proof Let New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 1
book:
4
books
cite this book:
- Integral Equations (Cambridge Tracts in Mathematics) by F. Smithies in Back Matter
- Nonlinear Analysis: The Herbert Amann Festschrift (Progress in Nonlinear Differential Equations and Their Applications) by Joachim Escher on page 729
- Sobolev Spaces, Volume 140, Second Edition (Pure and Applied Mathematics) by Robert A. Adams in Back Matter
- Function Spaces and Applications by David E. Edmunds on page 115
- Function Spaces, Interpolation Theory and Related Topics: Proceedings of the International Conference in Honour of Jaak Peetre on His 65th Birthday, ... ([De Gruyter Proceedings in Mathematics]) by Jaak Peetre in Back Matter
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