06089nam 22018135 450 991015474280332120190708092533.01-4008-8187-010.1515/9781400881871(CKB)3710000000631393(SSID)ssj0001651342(PQKBManifestationID)16425925(PQKBTitleCode)TC0001651342(PQKBWorkID)13732027(PQKB)10866502(MiAaPQ)EBC4738604(DE-B1597)468039(OCoLC)979968795(DE-B1597)9781400881871(EXLCZ)99371000000063139320190708d2016 fg engurcnu||||||||txtccrTopics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63), Volume 63 /Elias M. SteinPrinceton, NJ : Princeton University Press, [2016]©19701 online resource (160 pages)Annals of Mathematics Studies ;251Bibliographic Level Mode of Issuance: Monograph0-691-08067-4 Includes bibliographical references.Frontmatter -- Preface -- Contents -- Introduction -- Chapter I: Lie Groups (A Review) -- Chapter II: Littlewood-Paley Theory for a Compact Lie Group -- Chapter III: General Symmetric Diffusion Semi-Groups -- Chapter IV: The General Littlewood-Paley Theory -- Chapter V: Further Illustrations -- References -- Appendix (1985)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.Annals of mathematics studies ;Number 63.Harmonic analysisLittlewood-Paley theoryLie groupsSemigroupsAddition.Analytic function.Axiom.Boundary value problem.Central limit theorem.Change of variables.Circle group.Classification theorem.Commutative property.Compact group.Complex analysis.Convex set.Coset.Covering space.Derivative.Differentiable manifold.Differential geometry.Differential operator.Dimension (vector space).Dimension.Direct sum.E6 (mathematics).E7 (mathematics).E8 (mathematics).Elementary proof.Equation.Equivalence class.Existence theorem.Existential quantification.Fourier analysis.Fourier series.Fourier transform.Function space.General linear group.Haar measure.Harmonic analysis.Harmonic function.Hermite polynomials.Hilbert transform.Homogeneous space.Homomorphism.Ideal (ring theory).Identity matrix.Indecomposability.Integral transform.Invariant measure.Invariant subspace.Irreducibility (mathematics).Irreducible representation.Lebesgue measure.Legendre polynomials.Lie algebra.Lie group.Linear combination.Linear map.Local diffeomorphism.Markov process.Martingale (probability theory).Matrix group.Measurable function.Measure (mathematics).Multiple integral.Normal subgroup.One-dimensional space.Open set.Ordinary differential equation.Orthogonality.Orthonormality.Parseval's theorem.Partial differential equation.Probability space.Quadratic form.Rank of a group.Regular representation.Riemannian manifold.Riesz transform.Schur orthogonality relations.Scientific notation.Semigroup.Sequence.Special case.Stone–Weierstrass theorem.Sturm–Liouville theory.Subgroup.Subset.Summation.Tensor algebra.Tensor product.Theorem.Theory.Topological group.Topological space.Torus.Trigonometric polynomial.Trivial representation.Uniform convergence.Unitary operator.Unitary representation.Vector field.Vector space.Harmonic analysis.Littlewood-Paley theory.Lie groups.Semigroups.515.2433Stein Elias M., 41144Princeton University.DE-B1597DE-B1597BOOK9910154742803321Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63), Volume 632786624UNINA