Hans Triebel Book order

Continuing the exploration of function spaces, this volume serves as both a supplement to the "Theory of Function Spaces" trilogy and a companion to the textbook by D.D. Haroske and the author on distributions, Sobolev spaces, and elliptic equations. It enhances the foundational concepts established in the earlier works, offering deeper insights and advanced discussions relevant to the field, making it a valuable resource for scholars and students alike.

Focusing on the interplay between fractal geometry and Fourier analysis, this book explores the spectral properties of fractal (pseudo)differential operators. It highlights recent advancements in function space theory that connect to fractal methods, particularly in spectral problems related to degenerate pseudodifferential operators. The text provides insights into entropy numbers and eigenvalue distribution, presenting new techniques not widely covered in existing literature. Additionally, it serves as a continuation of previous works in the field, enriching the understanding of fractal analysis.

Deals with the theory of function spaces and with the developments related to the numerous applications of the theory of function spaces to some neighbouring areas such as numerics, signal processing and fractal analysis. This book discusses typical building blocks as (non-smooth) atoms, quarks, wavelet bases and wavelet frames

InhaltsverzeichnisI Decompositions of Functions.1 Introduction, heuristics, and preliminaries.2 Spaces on ? n: the regular case.3 Spaces on ? n: the general case.4 An application: the Fubini property.5 Spaces on domains: localization and Hardy inequalities.6 Spaces on domains. decompositions.7 Spaces on manifolds.8 Taylor expansions of distributions.9 Traces on sets, related function spaces and their decompositions.II Sharp Inequalities.10 Introduction: Outline of methods and results.11 Classical inequalities.12 Envelopes.13 The critical case.14 The super-critical case.15 The sub-critical case.16 Hardy inequalities.17 Complements.III Fractal Elliptic Operators.18 Introduction.19 Spectral theory for the fractal Laplacian.20 The fractal Dirichlet problem.21 Spectral theory on manifolds.22 Isotropic fractals and related function spaces.23 Isotropic fractal drums.IV Truncations and Semi-linear Equations.24 Introduction.25 Truncations.26 The Q-operator.27 Semi-linear equations; the Q-method.References.Symbois.