The Structure of Functions

Inhaltsverzeichnis

• I 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.