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Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63), Volume 63

Elias M. Stein

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, such as those arising in the study of the expansions coming from second order elliptic operators. A review of background material in Lie groups and martingale theory is included to make the monograph more accessible to the student.

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Schlagwörter

Lie algebra, Irreducibility (mathematics), Invariant subspace, Linear map, E7 (mathematics), Direct sum, Haar measure, Vector space, Stone–Weierstrass theorem, Equation, Legendre polynomials, Regular representation, Topological group, Differential geometry, Schur orthogonality relations, Compact group, Parseval's theorem, Commutative property, Ordinary differential equation, Semigroup, Harmonic analysis, Topological space, Unitary representation, Martingale (probability theory), Scientific notation, Tensor product, Sturm–Liouville theory, Riemannian manifold, Coset, Hermite polynomials, Linear combination, Fourier transform, Circle group, Lebesgue measure, Special case, Function space, Orthonormality, Dimension (vector space), Trigonometric polynomial, Differential operator, Dimension, Irreducible representation, Axiom, General linear group, Quadratic form, Harmonic function, Integral transform, E8 (mathematics), Unitary operator, E6 (mathematics), Ideal (ring theory), Central limit theorem, Riesz transform, Equivalence class, Partial differential equation, Summation, Analytic function, Fourier series, Theorem, Identity matrix, Existence theorem, Fourier analysis, Matrix group, Measure (mathematics), Change of variables, Classification theorem, Tensor algebra, Lie group, Homomorphism, Boundary value problem