Moebius-invariant algebras in balls

Walter Rudin

Displaying similar documents to “Moebius-invariant algebras in balls”

A finite multiplicity Helson-Lowdenslager-de Branges theorem

Sneh Lata, Meghna Mittal, Dinesh Singh (2010)

Studia Mathematica

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We prove two theorems. The first theorem reduces to a scalar situation the well known vector-valued generalization of the Helson-Lowdenslager theorem that characterizes the invariant subspaces of the operator of multiplication by the coordinate function z on the vector-valued Lebesgue space L²(;ℂⁿ). Our approach allows us to prove an equivalent version of the vector-valued Helson-Lowdenslager theorem in a completely scalar setting, thereby eliminating the use of range functions and partial...

A geometric approach to full Colombeau algebras

R. Steinbauer (2010)

Banach Center Publications

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We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view of the construction of the intrinsically defined algebra $\hat{} (M)$ on the manifold M given in [gksv].

A new invariant and parametric connected sum of embeddings

A. Skopenkov (2007)

Fundamenta Mathematicae

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We define an isotopy invariant of embeddings $N \to ℝ^{m}$ of manifolds into Euclidean space. This invariant together with the α-invariant of Haefliger-Wu is complete in the dimension range where the α-invariant could be incomplete. We also define parametric connected sum of certain embeddings (analogous to surgery). This allows us to obtain new completeness results for the α-invariant and the following estimation of isotopy classes of embeddings. In the piecewise-linear category, for a (3n-2m+2)-connected...

Linear combinations of generators in multiplicatively invariant spaces

Victoria Paternostro (2015)

Studia Mathematica

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Multiplicatively invariant (MI) spaces are closed subspaces of L²(Ω, ) that are invariant under multiplication by (some) functions in $L^{\infty} (Ω)$ ; they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of functions constructed by taking linear combinations of the generators of a finitely generated MI space is a new set of generators for the same space, and we give necessary and sufficient conditions...

Translation invariant forms on $L^{p} (G) (1 < p < \infty)$

Jean Bourgain (1986)

Annales de l'institut Fourier

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It is shown that if $G$ is a connected metrizable compact Abelian group and $1 < p < \infty$ , any (possibly discontinuous) translation invariant linear form on $L^{p} (G)$ is a scalar multiple of the Haar measure. This result extends the theorem of G.H. Meisters and W.M. Schmidt (J. Funct. Anal. 13 (1972), 407-424) on $L^{2} (G)$ . Our method permits in fact to consider any superreflexive translation invariant Banach lattice on $G$ , which is the adopted point of view. We study the representation of an element $f$ of this invariant...

On projections of $L^{\infty} (G)$ onto translation-invariant subspaces

W. Chojnacki (1978)

Colloquium Mathematicae

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On invariant, dual invariant and absolute formulas

Andrzej Mostowski

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CONTENTS Introduction..............................................................................................................................................................3 1. Lemmas concerning first order formulas.....................................................................................................5 2. Representability of recursively enumerable sets........................................................................................9 3. Simple theory of types.......................................................................................................................................10...

Uniform bounds for quotients of Green functions on $C^{1, 1}$ -domains

H. Hueber, M. Sieveking (1982)

Annales de l'institut Fourier

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Let $Δ u = Σ_{i} \frac{\partial^{2}}{\partial_{x_{i}}^{2}}$ , $L u = Σ_{i, j} a_{i j} \frac{\partial^{2}}{\partial x_{i} \partial x_{j}} u + Σ_{i} b_{i} \frac{\partial}{\partial x_{i}} u + c u$ be elliptic operators with Hölder continuous coefficients on a bounded domain $Ω \subset R^{n}$ of class $C^{1, 1}$ . There is a constant $c > 0$ depending only on the Hölder norms of the coefficients of $L$ and its constant of ellipticity such that $c^{- 1} G_{Δ}^{Ω} \leq G_{L}^{Ω} \leq c G_{Δ}^{Ω} on Ω \times Ω,$ where $γ_{Δ}^{Ω}$ (resp. $G_{L}^{Ω}$ ) are the Green functions of $Δ$ (resp. $L$ ) on $Ω$ .

Beurling-Figà-Talamanca-Herz algebras

Serap Öztop, Volker Runde, Nico Spronk (2012)

Studia Mathematica

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For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras $A_{p} (G, ω)$ . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We...

Automatic continuity of operators commuting with translations

J. Alaminos, J. Extremera, A. R. Villena (2006)

Studia Mathematica

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Let $τ_{X}$ and $τ_{Y}$ be representations of a topological group G on Banach spaces X and Y, respectively. We investigate the continuity of the linear operators Φ: X → Y with the property that $Φ \circ τ_{X} (t) = τ_{Y} (t) \circ Φ$ for each t ∈ G in terms of the invariant vectors in Y and the automatic continuity of the invariant linear functionals on X.

Division algebras that generalize Dickson semifields

Daniel Thompson (2020)

Communications in Mathematics

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We generalize Knuth’s construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension $2 s^{2}$ by doubling central division algebras of degree $s$ . Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

Pervasive algebras on planar compacts

Jan Čerych (1999)

Commentationes Mathematicae Universitatis Carolinae

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We characterize compact sets $X$ in the Riemann sphere $𝕊$ not separating $𝕊$ for which the algebra $A (X)$ of all functions continuous on $𝕊$ and holomorphic on $𝕊 ∖ X$ , restricted to the set $X$ , is pervasive on $X$ .