Projective representations of spaces of quasianalytic functionals

José Bonet; Reinhold Meise; Sergeĭ N. Melikhov

Displaying similar documents to “Projective representations of spaces of quasianalytic functionals”

Weighted $L^{\infty}$ -estimates for Bergman projections

José Bonet, Miroslav Engliš, Jari Taskinen (2005)

Studia Mathematica

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We consider Bergman projections and some new generalizations of them on weighted $L^{\infty} ()$ -spaces. A new reproducing formula is obtained. We show the boundedness of these projections for a large family of weights v which tend to 0 at the boundary with a polynomial speed. These weights may even be nonradial. For logarithmically decreasing weights bounded projections do not exist. In this case we instead consider the projective description problem for holomorphic inductive limits.

A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform

Sandra Pot (2007)

Studia Mathematica

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Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space . We show that if W and its inverse $W^{- 1}$ both satisfy a matrix reverse Hölder property introduced by Christ and Goldberg, then the weighted Hilbert transform $H : L ²_{W} (ℝ,) \to L ²_{W} (ℝ,)$ and also all weighted dyadic martingale transforms $T_{σ} : L ²_{W} (ℝ,) \to L ²_{W} (ℝ,)$ are bounded. We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform.

Weighted bounds for variational Fourier series

Yen Do, Michael Lacey (2012)

Studia Mathematica

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For 1 < p < ∞ and for weight w in $A_{p}$ , we show that the r-variation of the Fourier sums of any function f in $L^{p} (w)$ is finite a.e. for r larger than a finite constant depending on w and p. The fact that the variation exponent depends on w is necessary. This strengthens previous work of Hunt-Young and is a weighted extension of a variational Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses weighted adaptation of phase plane analysis and a weighted extension of a variational...

The Properties of the Weighted Space $H_{2, α}^{k} (Ω)$ and Weighted Set $W_{2, α}^{k} (Ω, δ)$

V.A. Rukavishnikov, E.V. Matveeva, E.I. Rukavishnikova (2018)

Communications in Mathematics

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We study the properties of the weighted space $H_{2, α}^{k} (Ω)$ and weighted set $W_{2, α}^{k} (Ω, δ)$ for boundary value problem with singularity.

The projective limit of the $H^{p}$ spaces

J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)

Colloquium Mathematicae

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Characterization of associate spaces of weighted Lorentz spaces with applications

Amiran Gogatishvili, Luboš Pick, Filip Soudský (2014)

Studia Mathematica

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We characterize associate spaces of weighted Lorentz spaces GΓ(p,m,w) and present some applications of this result including necessary and sufficient conditions for a Sobolev-type embedding into $L^{\infty}$ .

On the diametral dimension of weighted spaces of analytic germs

Michael Langenbruch (2016)

Studia Mathematica

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We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces $S ¹_{α}$ and $S ₁^{α}$ for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.

Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$

Josef Vala (1988)

Časopis pro pěstování matematiky

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Bases in spaces of analytic germs

Michael Langenbruch (2012)

Annales Polonici Mathematici

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We prove precise decomposition results and logarithmically convex estimates in certain weighted spaces of holomorphic germs near ℝ. These imply that the spaces have a basis and are tamely isomorphic to the dual of a power series space of finite type which can be calculated in many situations. Our results apply to the Gelfand-Shilov spaces $S ¹_{α}$ and $S ₁^{α}$ for α > 0 and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.

Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

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

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In this work we give a characterization of the projective invariant pseudometric $P$ , introduced by H. Wu, for a particular class of real $\mathbf{C}^{\infty}$ -manifolds; in view of this result, we study the group of projective transformations for the same class of manifolds and we determine the integrated pseudodistance $p$ of $P$ in open convex regular cones of $\mathbb{R}^{n}$ , endowed with the characteristic metric.

Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space

Jae Gil Choi, Sang Kil Shim (2023)

Czechoslovak Mathematical Journal

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We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space $(H, B, ν)$ . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space $B$ . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in...

Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

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

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Continuation of holomorphic functions with growth conditions and some of its applications

Alexander V. Abanin, Pham Trong Tien (2010)

Studia Mathematica

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We prove a generalization of the well-known Hörmander theorem on continuation of holomorphic functions with growth conditions from complex planes in $ℂ^{p}$ into the whole $ℂ^{p}$ . We apply this result to construct special families of entire functions playing an important role in convolution equations, interpolation and extension of infinitely differentiable functions from closed sets. These families, in their turn, are used to study optimal or canonical, in a certain sense, weight sequences defining...

Operational calculus and Fourier transform on Boehmians

V. Karunakaran, R. Roopkumar (2005)

Colloquium Mathematicae

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We define various operations on the space of ultra Boehmians like multiplication with certain analytic functions which are Fourier transforms of compactly supported distributions, polynomials, and characters $(e^{i s t}, s, t \in ℝ)$ , translation, differentiation. We also prove that the Fourier transform on the space of ultra Boehmians has all the operational properties as in the classical theory.

Boundedness of Riesz transforms on weighted Carleson measure spaces

Ming-Yi Lee (2012)

Studia Mathematica

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Let w be in the Muckenhoupt $A_{\infty}$ weight class. We show that the Riesz transforms are bounded on the weighted Carleson measure space $C M O_{w}^{p}$ , the dual of the weighted Hardy space $H_{w}^{p}$ , 0 < p ≤ 1.

The representation of multi-hypergraphs by set intersections

Stanisław Bylka, Jan Komar (2007)

Discussiones Mathematicae Graph Theory

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This paper deals with weighted set systems (V,,q), where V is a set of indices, $\subset 2^{V}$ and the weight q is a nonnegative integer function on . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V,,q) is defined to be an indexed family $R = {(R_{v})}_{v \in V}$ of subsets of a set S such that $| ⋂_{v \in E} R_{v} | = q (E)$ for each E ∈ . A necessary condition...

Gorenstein projective complexes with respect to cotorsion pairs

Renyu Zhao, Pengju Ma (2019)

Czechoslovak Mathematical Journal

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Let $(𝒜, ℬ)$ be a complete and hereditary cotorsion pair in the category of left $R$ -modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair $(𝒜, ℬ)$ are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair $(𝒜, ℬ)$ . As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion...

Centered weighted composition operators via measure theory

Mohammad Reza Jabbarzadeh, Mehri Jafari Bakhshkandi (2018)

Mathematica Bohemica

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We describe the centered weighted composition operators on $L^{2} (Σ)$ in terms of their defining symbols. Our characterizations extend Embry-Wardrop-Lambert’s theorem on centered composition operators.

Projective representations of $S_{n}$ : ring structure and inductive formulae

P. Hoffman (1990)

Banach Center Publications

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$^{\infty}$ -vectors and boundedness

Jan Stochel, F. H. Szafraniec (1997)

Annales Polonici Mathematici

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The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its $^{\infty}$ -vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.

A new characterization of projective special unitary group PSU $(5, q)$

Behnam Ebrahimzadeh (2024)

Commentationes Mathematicae Universitatis Carolinae

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Projective special unitary groups $PSU (5, q)$ , where $\frac{q^{4} - q^{3} + q^{2} - q + 1}{(5, q + 1)}$ is a prime, is uniquely determined by its order and the size of one conjugacy class.