Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends

✍ Scribed by B. M. Brown, M. S. P. Eastham (auth.), B. Malcolm Brown, Jan Lang, Ian G. Wood (eds.)

• Publisher: Birkhäuser Basel
• Year: 2012
• Tongue: English
• Leaves: 268
• Series: Operator Theory: Advances and Applications 219
• Edition: 1
• Category: Library

✦ Synopsis

This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.

✦ Table of Contents

Front Matter....Pages i-xii
Generalised Meissner Equations with an Eigenvalue-inducing Interface....Pages 1-20
On the HELP Inequality for Hill Operators on Trees....Pages 21-36
Measure of Non-compactness of Operators Interpolated by Limiting Real Methods....Pages 37-54
A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality....Pages 55-67
Dichotomy in Muckenhoupt Weighted Function Space: A Fractal Example....Pages 69-89
Lavrentiev’s Theorem and Error Estimation in Elliptic Inverse Problems....Pages 91-103
Two-weighted Norm Inequalities for the Double Hardy Transforms and Strong Fractional Maximal Functions in Variable Exponent Lebesgue Space....Pages 105-124
Modular Eigenvalues of the Dirichlet p (·)-Laplacian and Their Stability....Pages 125-137
Spectral Properties of Some Degenerate Elliptic Differential Operators....Pages 139-156
Continuous and Compact Embeddings of Bessel-Potential-Type Spaces....Pages 157-196
A Sequence of Zero Modes of Weyl–Dirac Operators and an Associated Sequence of Solvable Polynomials....Pages 197-209
A Szegő Limit Theorem for Operators with Discontinuous Symbols in Higher Dimensions: Widom’s Conjecture....Pages 211-231
On a Supremum Operator....Pages 233-242
Entropy Numbers of Quadratic Forms and Their Applications to Spectral Theory....Pages 243-262

✦ Subjects

Operator Theory