Author | Graham, Colin C. author |
---|---|
Title | Essays in Commutative Harmonic Analysis [electronic resource] / by Colin C. Graham, O. Carruth McGehee |
Imprint | New York, NY : Springer New York, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-9976-9 |
Descript | 464 p. online resource |
1 The Behavior of Transforms -- 1.1 Introduction -- 1.2 The Idempotents in the Measure Algebra -- 1.3 Paul Cohenโs Theorem on the Norms of Idempotents -- 1.4 Transforms of Continuous Measures -- 1.5 The Two Sides of a Fourier Transform -- 1.6 Transforms of Rudin-Shapiro Type -- 1.7 A Separable Banach Space That Has No Basis -- 1.8 Restrictions of Fourier-Stieltjes Transforms to Sets of Positive Haar Measure -- 2 A Proof That the Union of Two Helson Sets Is a Helson Set -- 2.1 Introduction -- 2.2 Definition of the Functions ?N -- 2.3 Transfering the Problem from One Group to Another -- 2.4 Proof of Theorem 2.1.3 -- 2.5 Remarks and Credits -- 3 Harmonic Synthesis -- 3.1 Introduction -- 3.2 When Synthesis Succeeds -- 3.3 When Synthesis Fails -- 1.2 Transducers for long term hemodynamic signals monitoring -- 4 Sets of Uniqueness, Sets of Multiplicity -- 4.1 Introduction -- 4.2 The Support of a Pseudomeasure -- 4.3 The Weak * Closure of I(E) -- 4.4 An M1-Set That Is Not an Mo-Set -- 4.5 Results about Helson Sets and Kronecker Sets -- 4.6 M-Sets Whose Helson Constant Is One -- 4.7 Independent Mo-Sets -- 5 A Brief Introduction to Convolution Measure Algebras -- 5.1 Elementary Properties -- 5.2 L-Subalgebras and L-Ideals -- 5.3 Critical Point Theory and a Proof of the Idempotent Theorem -- 5.4 A Guide for Further Study -- 6 Independent Power Measures -- 6.1 Introduction and Initial Results -- 6.2 Measures on Algebraically Scattered Sets -- 6.3 Measures on Dissociate Sets -- 6.4 Infinite Product Measures -- 6.5 General Results on Infinite Convolutions -- 6.6 Bernoulli Convolutions -- 6.7 Coin Tossings -- 6.8 Mo(G) Contains Tame i.p. Measures -- 7 Riesz Products -- 7.1 Introduction and Initial Results -- 7.2 Orthogonality Relations for Riesz Products -- 7.3 Most Riesz Products Are Tame -- 7.4 A Singular Measure in Mo(G) That Is Equivalent to Its Square -- 7.5 A Multiplier Theorem and the Support of Singular Fourier-Stieltjes Transforms -- 7.6 Small Subsets of Z That Are Dense in bZ -- 7.7 Non-trivial Idempotents in B(E) for E ? Z -- 8 The ล ilov Boundary, Symmetric Ideals, and Gleason Parts of ?M(G) -- 8.1 Introduction -- 8.2 The ล ilov Boundary of M(G) -- 8.3 Some Translation Theorems -- 8.4 Non-symmetric Maximal Ideals in M(G) -- 8.5 Point Derivations and Strong Boundary Points for M(G) -- 8.6 Gleason Parts for Convolution Measure Algebras -- 9 The Wiener-Lรฉvy Theorem and Some of Its Converses -- 9.1 Introduction -- 9.2 Proof of the Wiener-Lรฉvy Theorem and Marcinkiewiczโs Theorem -- 9.3 Converses to the Wiener-Lรฉvy Theorem -- 9.4 Functions Operating in B(?) -- 9.5 Functions Operating in Bo(?) -- 9.6 Functions Operating on Norm One Positive-Definite Functions -- 10 The Multiplier Algebras Mp(?), and the Theorem of Zafran -- 10.1 Introduction -- 10.2 The Basic Theory of the Algebras Mp(?) -- 10.3 Zafranโs Theorem about the Algebra Mpo(Z) -- 11 Tensor Algebras and Harmonic Analysis -- 11.1 Introduction and Initial Results -- 11.2 Transfer Methods: Harmonic Synthesis and Non-finitely Generated Ideals in L1(G) -- 11.3 Sets of Analyticity and Tensor Algebras -- 11.4 Infinite Tensor Products and the Saucer Principle -- 11.5 Continuity Conditions for Membership in V(T,T) -- 11.6 Sidon Constants of Finite Sets for Tensor Algebras and Group Algebras -- 11.7 Automorphisms of Tensor Algebras -- 11.8 V-Sidon and V-Interpolation Sets -- 11.9 Tilde Tensor Algebras -- 12 Tilde Algebras -- 12.1 Introduction -- 12.2 Subsets of Discrete Groups -- 12.3 The Connection with Synthesis -- 12.4 Sigtuna Sets -- 12.5 An Example in which A(E) Is a Dense Proper Subspace of $$\tilde{A}$$(E) -- 13 Unsolved Problems -- 13.1 Dichotomy -- 13.2 Finite Sets -- 13.3 Isomorphisms between Quotients of A(G) -- 13.4 The Rearrangements Question of N. N. Lusin -- 13.5 Continuity of Linear Operators on L1(R) -- 13.6 p-Helson Sets -- 13.7 Questions of Atzmon on Translation Invariant Subspaces of LP and Co -- 13.8 Questions on Subsets E of the Integer Group -- 13.9 Questions on Sets of Synthesis -- 13.10 Characterizing Sidon Sets in Certain Groups -- 13.11 Subalgebras of L1 -- 13.12 ?(p)-Sets and Multipliers -- 13.13 Identifying the Maximal Ideal Spaces of Certain L-Subalgebras of M(G) -- 13.14 A Question of Katznelson on Measures with Real Spectra -- 13.15 The Support Group ofa Tame Measure -- 13.16 The ล ilov Boundary of M(G) -- 13.17 Taylorโs Theorems -- 13.18 Two Factorization Questions -- 13.19 Questions about Tensor Algebras -- 13.20 Other Question Lists -- A.1. Riesz Products in Brief -- A.3. A Proof That Singletons Obey Synthesis, and How -- A.4. S. Bernsteinโs Inequality -- A.S. Triangles and Trapezoids -- A.6. Convolution and Relative Absolute Continuity -- A.7. An Extension Theorem for Fourier-Stieltjes Transforms -- References