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Quantitative Analysis in Sobolev Imbedding Theorems and Applications to Spectral Theory (American Mathematical Society Translations Series 2)
Quantitative Analysis in Sobolev Imbedding Theorems and Applications to Spectral Theory (American Mathematical Society Translations Series 2)
Date: 11 June 2011, 02:01
The lectures in this book are devoted to quantitative analysis in connection with Sobolev imbedding theorems for the function spaces W which Sobolev introduced. The fundamental significance of the Sobolev imbedding theorems in
analysis and mathematical physics is well known. Usually by imbedding theorems we mean "qualitative" assertions concerning continuity or compactness of an imbedding of one class W into another. Our principal goal is a "quantitative" investigation of the corresponding imbedding operators, which usually turn out to be compact. The conventional quantitative characteristics of compact imbeddings are e-entropy and u-widths of the corresponding unit sphere.

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