Inductive extreme non-Arens regularity of the Fourier algebra A(G)

Zhiguo Hu

Displaying similar documents to “Inductive extreme non-Arens regularity of the Fourier algebra A(G)”

Operator Segal algebras in Fourier algebras

Brian E. Forrest, Nico Spronk, Peter J. Wood (2007)

Studia Mathematica

Similarity:

Let G be a locally compact group, A(G) its Fourier algebra and L¹(G) the space of Haar integrable functions on G. We study the Segal algebra S¹A(G) = A(G) ∩ L¹(G) in A(G). It admits an operator space structure which makes it a completely contractive Banach algebra. We compute the dual space of S¹A(G). We use it to show that the restriction operator ${u \mapsto u |}_{H} : S ¹ A (G) \to A (H)$ , for some non-open closed subgroups H, is a surjective complete quotient map. We also show that if N is a non-compact closed subgroup,...

Un ensemble remarquable du point de vue de l’analyse de Fourier sur $Q_{p}$

J. P. Schreiber (1971)

Colloquium Mathematicae

Similarity:

The $L^{p}$ -Helmholtz projection in finite cylinders

Tobias Nau (2015)

Czechoslovak Mathematical Journal

Similarity:

In this article we prove for $1 < p < \infty$ the existence of the $L^{p}$ -Helmholtz projection in finite cylinders $Ω$ . More precisely, $Ω$ is considered to be given as the Cartesian product of a cube and a bounded domain $V$ having $C^{1}$ -boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in $Ω$ is solved, which implies existence and a representation of the $L^{p}$ -Helmholtz projection...

Operator Figà-Talamanca-Herz algebras

Volker Runde (2003)

Studia Mathematica

Similarity:

Let G be a locally compact group. We use the canonical operator space structure on the spaces $L^{p} (G)$ for p ∈ [1,∞] introduced by G. Pisier to define operator space analogues $O A_{p} (G)$ of the classical Figà-Talamanca-Herz algebras $A_{p} (G)$ . If p ∈ (1,∞) is arbitrary, then $A_{p} (G) \subset O A_{p} (G)$ and the inclusion is a contraction; if p = 2, then OA₂(G) ≅ A(G) as Banach spaces, but not necessarily as operator spaces. We show that $O A_{p} (G)$ is a completely contractive Banach algebra for each p ∈ (1,∞), and that $O A_{q} (G) \subset O A_{p} (G)$ completely contractively...

A transplantation theorem for ultraspherical polynomials at critical index

J. J. Guadalupe, V. I. Kolyada (2001)

Studia Mathematica

Similarity:

We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the “boundary” Lorentz space $ℒ_{λ}$ corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients $c ₙ^{(λ)} (f)$ of $ℒ_{λ}$ -functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any $f \in ℒ_{λ}$ the series $\sum_{n = 1}^{\infty} c ₙ^{(λ)} (f) c o s n θ$ is the Fourier series of some function φ ∈ ReH¹ with ${| | φ | |}_{R e H ¹} {\leq c | | f | |}_{ℒ_{λ}}$ . ...

On $L^{p}$ integrability and convergence of trigonometric series

Dansheng Yu, Ping Zhou, Songping Zhou (2007)

Studia Mathematica

Similarity:

We first give a necessary and sufficient condition for $x^{- γ} ϕ (x) \in L^{p}$ , 1 < p < ∞, 1/p - 1 < γ < 1/p, where ϕ(x) is the sum of either $\sum_{k = 1}^{\infty} a_{k} c o s k x$ or $\sum_{k = 1}^{\infty} b_{k} s i n k x$ , under the condition that λₙ (where λₙ is aₙ or bₙ respectively) belongs to the class of so called Mean Value Bounded Variation Sequences (MVBVS). Then we discuss the relations among the Fourier coefficients λₙ and the sum function ϕ(x) under the condition that λₙ ∈ MVBVS, and deduce a sharp estimate for the weighted modulus of continuity of ϕ(x)...

Analytical theory of nonlinear oscillations $X$ : some classes of equations $\ddot{x}+g(x)=0$ with no finite Fourier series solution

Chike Obi (1979)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Si dimostra che l'equazione considerata nel titolo ammette soluzioni periodiche rappresentabili da una serie di Fourier con un numero finito di termini solo se $g(x)$ è lineare.

Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations

Fabio Nicola (2010)

Studia Mathematica

Similarity:

We study Fourier integral operators of Hörmander’s type acting on the spaces $ℱ L^{p} {(ℝ^{d})}_{c o m p}$ , 1 ≤ p ≤ ∞, of compactly supported distributions whose Fourier transform is in $L^{p}$ . We show that the sharp loss of derivatives for such an operator to be bounded on these spaces is related to the rank r of the Hessian of the phase Φ(x,η) with respect to the space variables x. Indeed, we show that operators of order m = -r|1/2-1/p| are bounded on $ℱ L^{p} {(ℝ^{d})}_{c o m p}$ if the mapping $x \mapsto \nabla_{x} Φ (x, η)$ is constant on the fibres, of codimension r,...

Solution of a functional equation on compact groups using Fourier analysis

Abdellatif Chahbi, Brahim Fadli, Samir Kabbaj (2015)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

Let $G$ be a compact group, let $n \in N ∖ {0, 1}$ be a fixed element and let $σ$ be a continuous automorphism on $G$ such that $σ^{n} = I$ . Using the non-abelian Fourier transform, we determine the non-zero continuous solutions $f : G \to C$ of the functional equation $f (x y) + \sum_{k = 1}^{n - 1} f (σ^{k} (y) x) = n f (x) f (y), x, y \in G,$ in terms of unitary characters of $G$ .

Trivialization of $𝒞 (X)$ -algebras with strongly self-absorbing fibres

Marius Dadarlat, Wilhelm Winter (2008)

Bulletin de la Société Mathématique de France

Similarity:

Suppose $A$ is a separable unital $𝒞 (X)$ -algebra each fibre of which is isomorphic to the same strongly self-absorbing and $K_{1}$ -injective $C^{*}$ -algebra $𝒟$ . We show that $A$ and $𝒞 (X) \otimes 𝒟$ are isomorphic as $𝒞 (X)$ -algebras provided the compact Hausdorff space $X$ is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.

Convergence of greedy approximation II. The trigonometric system

S. V. Konyagin, V. N. Temlyakov (2003)

Studia Mathematica

Similarity:

We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form $G ₘ (f) : = \sum_{k \in Λ} f ̂ (k) e^{i (k, x)}$ , where $Λ \subset ℤ^{d}$ is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in...

On the vector-valued Fourier transform and compatibility of operators

In Sook Park (2005)

Studia Mathematica

Similarity:

Let be a locally compact abelian group and let 1 < p ≤ 2. ’ is the dual group of , and p’ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform $F^{}$ if $F^{} \otimes T : L_{p} () \otimes X \to L_{p^{'}} (^{'}) \otimes Y$ admits a continuous extension $[F^{}, T] : [L_{p} (), X] \to [L_{p^{'}} (^{'}), Y]$ . Let $ℱ T_{p}^{}$ denote the collection of such T’s. We show that $ℱ T_{p}^{ℝ \times} = ℱ T_{p}^{ℤ \times} = ℱ T_{p}^{ℤ ⁿ \times}$ for any and positive integer n. Moreover, if the factor group of by its identity component is a direct sum of a torsion-free group and a finite group with discrete topology then...

Multiple solutions to a perturbed Neumann problem

Giuseppe Cordaro (2007)

Studia Mathematica

Similarity:

We consider the perturbed Neumann problem ⎧ -Δu + α(x)u = α(x)f(u) + λg(x,u) a.e. in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where Ω is an open bounded set in $ℝ^{N}$ with boundary of class C², $α \in L^{\infty} (Ω)$ with $e s s i n f_{Ω} α > 0$ , f: ℝ → ℝ is a continuous function and g: Ω × ℝ → ℝ, besides being a Carathéodory function, is such that, for some p > N, $s u p_{| s | \leq t} | g (\cdot, s) | \in L^{p} (Ω)$ and $g (\cdot, t) \in L^{\infty} (Ω)$ for all t ∈ ℝ. In this setting, supposing only that the set of global minima of the function $1 / 2 ξ ² - \int_{0}^{ξ} f (t) d t$ has M ≥ 2 bounded connected components, we prove that, for all λ ∈ ℝ small enough,...

The Gibbs phenomenon and Lebesgue constants for regular $A (λ)$ means

V. Swaminathan (1977)

Matematički Vesnik

Similarity:

Multifractal analysis of the divergence of Fourier series

Frédéric Bayart, Yanick Heurteaux (2012)

Annales scientifiques de l'École Normale Supérieure

Similarity:

A famous theorem of Carleson says that, given any function $f \in L^{p} (𝕋)$ , $p \in (1, + \infty)$ , its Fourier series $(S_{n} f (x))$ converges for almost every $x \in 𝕋$ . Beside this property, the series may diverge at some point, without exceeding $O (n^{1 / p})$ . We define the divergence index at $x$ as the infimum of the positive real numbers $β$ such that $S_{n} f (x) = O (n^{β})$ and we are interested in the size of the exceptional sets $E_{β}$ , namely the sets of $x \in 𝕋$ with divergence index equal to $β$ . We show that quasi-all functions in $L^{p} (𝕋)$ have a multifractal behavior with respect to...

Pointwise regularity associated with function spaces and multifractal analysis

Stéphane Jaffard (2006)

Banach Center Publications

Similarity:

The purpose of multifractal analysis of functions is to determine the Hausdorff dimensions of the sets of points where a function (or a distribution) f has a given pointwise regularity exponent H. This notion has many variants depending on the global hypotheses made on f; if f locally belongs to a Banach space E, then a family of pointwise regularity spaces $C_{E}^{α} (x ₀)$ are constructed, leading to a notion of pointwise regularity with respect to E; the case $E = L^{\infty}$ corresponds to the usual Hölder regularity,...

Internally club and approachable for larger structures

John Krueger (2008)

Fundamenta Mathematicae

Similarity:

We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of $P_{κ} (X)$ , where κ ⊆ X. Suppose μ < κ, $μ^{< μ} = μ$ , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in ${[H (λ)]}^{μ ⁺}$ which are internally club but not internally approachable.

Projection of Wreath Products of Lie Algebras

Alexander A. Lašhi (1980)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Sia $K$ un dominio a ideali principali, che non sia un campo e sia $L$ un'algebra di Lie su $K$ . Principale risultato: Se $L=A\,wr\,B$ , cioè se $L$ è prodotto intrecciato delle algebre di Lie precarie $A$ e $B$ , ogni isomorfismo reticolare normale di $L$ è indotto da un isomorfismo. Si prova anche, mediante un esempio, che per le algebre sopra un campo il teorema non è vero.

The harmonic Cesáro and Copson operators on the spaces $L^{p} (ℝ)$ , 1 ≤ p ≤ 2

Ferenc Móricz (2002)

Studia Mathematica

Similarity:

The harmonic Cesàro operator is defined for a function f in $L^{p} (ℝ)$ for some 1 ≤ p < ∞ by setting $(f) (x) : = \int_{x}^{\infty} (f (u) / u) d u$ for x > 0 and $(f) (x) : = - \int_{- \infty}^{x} (f (u) / u) d u$ for x < 0; the harmonic Copson operator ℂ* is defined for a function f in $L ¹_{l o c} (ℝ)$ by setting $* (f) (x) : = (1 / x) \int^{x ₀} f (u) d u$ for x ≠ 0. The notation indicates that ℂ and ℂ* are adjoint operators in a certain sense. We present rigorous proofs of the following two commuting relations: (i) If $f \in L^{p} (ℝ)$ for some 1 ≤ p ≤ 2, then ${((f))}^{\land} (t) = * (f ̂) (t)$ a.e., where f̂ denotes the Fourier transform of f. (ii) If $f \in L^{p} (ℝ)$ for some 1 < p ≤ 2, then...

Infinitely many positive solutions for the Neumann problem involving the p-Laplacian

Giovanni Anello, Giuseppe Cordaro (2003)

Colloquium Mathematicae

Similarity:

We present two results on existence of infinitely many positive solutions to the Neumann problem ⎧ $- Δ_{p} u + λ (x) {| u |}^{p - 2} u = μ f (x, u)$ in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where $Ω \subset ℝ^{N}$ is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, $λ \in L^{\infty} (Ω)$ with $e s s i n f_{x \in Ω} λ (x) > 0$ and f: Ω × ℝ → ℝ is a Carathéodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.

Singularity categories of skewed-gentle algebras

Xinhong Chen, Ming Lu (2015)

Colloquium Mathematicae

Similarity:

Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let $(Q^{s g}, I^{s g})$ and $(Q^{g}, I^{g})$ be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra $K Q^{s g} / ⟨ I^{s g} ⟩$ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of $K Q^{g} / ⟨ I^{g} ⟩$ . As a corollary, we find that $g l d i m K Q^{s g} / ⟨ I^{s g} ⟩ < \infty$ if and only if $g l d i m K Q / ⟨ I ⟩ < \infty$ if and only if $g l d i m K Q^{g} / ⟨ I^{g} ⟩ < \infty$ .

Well-posedness of second order degenerate differential equations in vector-valued function spaces

Shangquan Bu (2013)

Studia Mathematica

Similarity:

Using known results on operator-valued Fourier multipliers on vector-valued function spaces, we give necessary or sufficient conditions for the well-posedness of the second order degenerate equations (P₂): d/dt (Mu’)(t) = Au(t) + f(t) (0 ≤ t ≤ 2π) with periodic boundary conditions u(0) = u(2π), (Mu’)(0) = (Mu’)(2π), in Lebesgue-Bochner spaces $L^{p} (, X)$ , periodic Besov spaces $B_{p, q}^{s} (, X)$ and periodic Triebel-Lizorkin spaces $F_{p, q}^{s} (, X)$ , where A and M are closed operators in a Banach space X satisfying D(A) ⊂ D(M)....

Rearrangement of coefficients of Fourier series on $S U_{2}$

Giancarlo Travaglini (1987)

Colloquium Mathematicae

Similarity:

On the persistence of decorrelation in the theory of wave turbulence

Anne-Sophie de Suzzoni (2013)

Journées Équations aux dérivées partielles

Similarity:

We study the statistical properties of the solutions of the Kadomstev-Petviashvili equations (KP-I and KP-II) on the torus when the initial datum is a random variable. We give ourselves a random variable $u_{0}$ with values in the Sobolev space $H^{s}$ with $s$ big enough such that its Fourier coefficients are independent from each other. We assume that the laws of these Fourier coefficients are invariant under multiplication by $e^{i θ}$ for all $θ \in ℝ$ . We investigate about the persistence of the decorrelation...

Factoriality of von Neumann algebras connected with general commutation relations-finite dimensional case

Ilona Królak (2006)

Banach Center Publications

Similarity:

We study a certain class of von Neumann algebras generated by selfadjoint elements $ω_{i} = a_{i} + a ⁺_{i}$ , where $a_{i}, a ⁺_{i}$ satisfy the general commutation relations: $a_{i} a ⁺_{j} = \sum_{r, s} t_{j}^{i} r_{s} a ⁺_{r} a_{s} + δ_{i j} I d$ . We assume that the operator T for which the constants $t_{j}^{i} r_{s}$ are matrix coefficients satisfies the braid relation. Such algebras were investigated in [BSp] and [K] where the positivity of the Fock representation and factoriality in the case of infinite dimensional underlying space were shown. In this paper we prove that under certain conditions on the...

Fourier approximation and embeddings of Sobolev spaces

D. E. Edmunds, V. B. Moscatelli

Similarity:

CONTENTSIntroduction............................................................................................................ 51. Preliminaries............................................................................................................. 82. Embedding into $W^{m, p} (Ω)$ into $L^{S} (Ω)$ (n>1).......................................... 103. The case n = 1.......................................................................................................... 284. Embedding $W^{m, p} (Ω)$ into $L^{φ} (Ω)$ ...............................................................