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39 results on '"Petkova, Violeta"'

1. Multipliers and Wiener-Hopf operators on weighted L^p spaces

Author

Petkova, Violeta

Subjects
Mathematics - Functional Analysis
Abstract

We study the operators T on the weighted space L^p commuting either with the right translations St or left translations P^+S_{-t} and we establish the existence of a symbol of T. We characterize completely the spectrum of St. We obtain a similar result for the spectrum of P^+S_{-t} and some spectral results for the bounded operators commuting with (St), t>0 or with (P^+St), t<0.

Published
2011

2. Spectral results for operators commuting with translations on Banach spaces of sequences on Z^k and Z^+

Author

Petkova, Violeta

Subjects
Mathematics - Spectral Theory, 47B37
Abstract

We study the spectrum of multipliers (bounded operators commuting with the shift operator S) on Banach spaces of sequences on Z and the spectrum of operators commuting with the shift on Banach spaces of sequences on Z^+.We generalize the results for multipliers on Banach spaces of sequences on Z^k.

Published
2011

3. Spectra of translations and Wiener-Hopf operators on Lw^2(R^+)

Author

Petkova, Violeta

Subjects
Mathematics - Functional Analysis
Abstract

We study the bounded operators on weighted spaces Lw^2 on R^+ commuting either with the right translations St or left translations and we establish the existence of a symbol for these operators. We characterize completely the spectrum of St. We give also a spectral results for the left translations and for the bounded operators commuting with the semi-group (St) or with the semi-group of the left translations.

Published
2011

4. Multipliers on Hilbert spaces of functions on R

Author

Petkova, Violeta

Subjects
Mathematics - Functional Analysis, 42A45
Abstract

For a Hilbert space H included in L^1_{loc} (R) of functions on $R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L^2(R) as well as our previous result for multipliers in weighted space Lw^2(R). Moreover, we obtain a description of the spectrum of S.

Published
2009

5. Multipliers and Toeplitz operators on Banach spaces of sequences

Author

Petkova, Violeta

Subjects
Mathematics - Functional Analysis, 47B37
Abstract

We prove that every multiplier M (bounded operator commuting with the shift operator) on a large class of Banach spaces of sequences on Z is associated to a function essentially bounded by the norm of M on the spectrum of S.

Published
2006

6. Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space

Author

Petkova, Violeta

Subjects
Mathematics - Functional Analysis
Abstract

A Wiener-Hopf operator on a Banach space of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf operators on a large class of functions on R+ with values in a separable Hilbert space.

Published
2006

18. Problèmes spectraux pour des opérateurs qui commutent avec les translations

Author

Petkova, Violeta, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Université de Lorraine, Jean Esterle, and Petkova, Violeta

Subjects
multiplicateutrs, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], operators, spectre, opérateur, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], translations
Abstract

Ce mémoire étudie divers problèmes spectraux concernant les opérateurs qui communtes avec des transalations sur différents esapces fonctionnelles, des opérateurs de Toeplitz et de Wiener-Hofp

Published
2014

19. Multipliers on a Hilbert Space of Functions on R

Author

Petkova, Violeta

Subjects
Multipliers, Spectrum
Abstract

2000 Mathematics Subject Classification: 42A45., For a Hilbert space H ⊂ L1loc(R) of functions on R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L2(R) as well as our previous result for multipliers in weighted space L2ω(R). Moreover, we obtain a description of the spectrum of S.

Published
2016

20. Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space

Author

Petkova, Violeta, Laboratoire Bordelais d'Analyse et Géométrie (LaBAG), and Université Sciences et Technologies - Bordeaux 1-Centre National de la Recherche Scientifique (CNRS)

Subjects
Multipliers, Spaces of Vector-Valued Functions, Translations, 43A22, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Abstract

We prove a representation theorem for bounded operators commuting with translations on L2ω(G,H), where G is a locally compact abelian group, H is a Hilbert space and ω is a weight on G. Moreover, in the particular case when G = R, we characterize completely the spectrum of the shift operator S1,ω on Lω2(R,H)., 2000 Mathematics Subject Classification: Primary 43A22, 43A25.

Published
2016

21. Spectra of the translations and Wiener-Kopf operators on $Lw^(R^+)$

Author

Petkova, Violeta, Institut Élie Cartan de Lorraine (IECL), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2014

22. Spectral theorem for multipliers on Lw^2(R)

Author

Petkova, Violeta, Petkova, Violeta, Laboratoire de Mathématiques et Applications de Metz (LMAM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)

Subjects
[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Abstract

We study the spectrum of a class of multipliers (operators commuting with translations on Lw^2(\R).

Published
2008

25. Multiplier on Banach spaces of functions on a locally compact Abelian group

Author

Petkova, Violeta, Laboratoire Bordelais d'Analyse et Géométrie (LaBAG), Université Sciences et Technologies - Bordeaux 1-Centre National de la Recherche Scientifique (CNRS), and Vrit, Catherine

Subjects
[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], generalized Fourier transform, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], ComputingMilieux_MISCELLANEOUS, Spectrum of translation operators
Abstract

International audience

Published
2007

26. Multiplicateurs sur les espaces de Banach de fonctions sur un groupe localement compact abélien

Author

Petkova, Violeta, Laboratoire Bordelais d'Analyse et Géométrie (LaBAG), Université Sciences et Technologies - Bordeaux 1-Centre National de la Recherche Scientifique (CNRS), Université Sciences et Technologies - Bordeaux I, and Jean Esterle(esterle@math.u-bordeaux1.fr)

Subjects
multiplicateurs, opérateurs de Wiener-Hopf, opérateurs de Toeplitz, transformée de Fourier, [MATH]Mathematics [math], translations
Abstract

We study the multipliers, i.e. the bounded operators commuting with the translations on a space of functions on a locally compact abelian group G. For every multiplier, we obtain an essentially bounded symbol on a set of continuous morphisms on G related to the joint spectrum of the translations. We also obtain analogous results for the Wiener-Hopf operators (resp. Toeplitz operators) on spaces of functions on R+ (resp. Z+).; On étudie les multiplicateurs, c'est-à-dire les opérateurs bornés qui commutent avec les translations sur un espace de fonctions sur un groupe localement compact abélien G. On obtient pour tout multiplicateur un symbole essentiellement borné sur un ensemble de morphismes continus sur G, lié au spectre simultané des translations. Nous établissons aussi des résultats analogues pour les opérateurs de Wiener-Hopf (resp. Toeplitz) sur des espaces de fonctions sur R+ (resp. Z+).

Published
2005

27. Wiener-Hopf operators on L2w(R+)

Author

PETKOVA, Violeta, Laboratoire Bordelais d'Analyse et Géométrie (LaBAG), and Université Sciences et Technologies - Bordeaux 1-Centre National de la Recherche Scientifique (CNRS)

Subjects
Multipliers, translation invariant subspaces, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], ComputingMilieux_MISCELLANEOUS, Wiener-Hopf operators
Abstract

International audience

Published
2005

33. SPECTRA OF THE TRANSLATIONS AND WIENER-HOPF OPERATORS ON Lω²(R+).

Author

PETKOVA, VIOLETA

Subjects
*SPECTRAL theory, *WIENER-Hopf operators, *MATHEMATICAL bounds, *EXISTENCE theorems, *SEMIGROUPS (Algebra), *MATHEMATICAL analysis
Abstract

We study bounded operators T on the weighted space Lω²(R+) commuting either with the "right shift operators" (Rt)t≥0 or "left shift operators" (L-t)t≥0, and we establish the existence of a symbol μ of T. We characterize completely the spectrum σ(Rt) of the operator Rt proving that σ(Rt) = {z ∈ C : |z| ≤ eα0t}, where α0 is the growth bound of (Rt)t≥0. We obtain a similar result for the spectrum of L-t, t >0. Moreover, for a bounded operator T commuting with Rt, t ≥ 0, we establish the inclusion μ(O) ⊂ σ(T), where O = {z ∈ C : Imz < α0}. [ABSTRACT FROM AUTHOR]

Published
2014
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34. Multipliers and Wiener-Hopf operators on weighted L spaces.

Author

Petkova, Violeta

Abstract

We study multipliers M (bounded operators commuting with translations) on weighted spaces L(ℝ), and establish the existence of a symbol µ for M, and some spectral results for translations S and multipliers. We also study operators T on the weighted space L(ℝ) commuting either with the right translations S, t ∈ ℝ, or left translations P S, t ∈ ℝ, and establish the existence of a symbol µ of T. We characterize completely the spectrum σ( S) of the operator S proving that where α is the growth bound of ( S). A similar result is obtained for the spectrum of ( P S), t ≥ 0. Moreover, for an operator T commuting with S, t ≥ 0, we establish the inclusion [Figure not available: see fulltext.], where $\mathcal{O}$ = { z ∈ ℂ: Im z < α}. [ABSTRACT FROM AUTHOR]

Published
2013
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35. Symbole d'un multiplicateur sur <f>Lω2(R)</f>

Author

Petkova, Violeta

Subjects
*MULTIPLIERS (Mathematical analysis), *FUNCTIONAL analysis, *BOUNDARY value problems, *OPERATOR theory
Abstract

Let Lω2(R) be a weighted space with weight ω. In this paper we show that for every bounded operator T on Lω2(R) which commutes with translations, and for every a∈Iω, there exists a function νa∈L∞(R) such that Here (g)a denotes the function x↠g(x)eax for g∈Lω2(R) and Iω=[lnRω-,lnRω+], where Rω+ is the spectral radius of the bilateral shift S :f(x)↠f(x-1) on Lω2(R), while 1/Rω- is the spectral radius of S-1. Moreover there exists a constant Cω depending on ω such that ǁνaǁ∞⩽CωǁTǁ for every a∈Iω. If Rω-, there exists a bounded holomorphic function ν on Åω:={z∈C∣Imz∈&Iring;ω}, such that Tf=ν&fcirc;, ∀f∈D(R) and ǁνǁ∞⩽CωǁTǁ, where Tf(a+ix)=(Tf)a(x) for a∈&Iring;ω. [Copyright &y& Elsevier]

Published
2004
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36. Wiener-Hopf operators on <img src="/fulltext-image.asp?format=htmlnonpaginated&src=RK4X567X286U7723_html\13_2004_Article_1167_TeX2GIFIEq1.gif" border="0" alt="$L_{\omega}^{2}(\mathbb{R}^{+})$" />

Author

Petkova, Violeta

Abstract

Abstract. Let "$L_{\omega}^{2}(\mathbb{R}^{+})$" be a weighted space with weight ?. In this paper we show that for every Wiener-Hopf operator T on "$L_{\omega}^{2}(\mathbb{R}^{+})$" and for every a ?I?, there exists a function "$v_a such that $$(Tf)_a = P^ + \mathcal{F}^{ - 1} (v_a \widehat{(f)_a }),$$ for all "$f Here (g)a denotes the function x ? g(x)eax for "$g and "$I_\omega where R?+ is the spectral radius of the shift S : f(x) ? f(x-1) on "$L_{\omega}^{2}(\mathbb{R}^{+}),$" while "$\frac{1}{R_{\omega}^{-}}$" is the spectral radius of the backward shift S-1 : f(x) ? (P+f)(x+1) on "$L_{\omega}^{2}(\mathbb{R}^{+}).$" Moreover, there exists a constant C?, depending on ?, such that "$||v_a for every a ?I?. If R?- < R?+, we prove that there exists a bounded holomorphic function v on "${\mathop such that for "$a the function va is the restriction of v on the line "$\{z

Published
2005
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39. Opérateurs de Toeplitz sur l'espace de Bergman harmonique et opérateurs de Teoplitz tronqués de rang fini

Author

RANDRIAMAHALEO, Fanilo Rajaofetra, Strouse, Elizabeth, Rajoelina, Michel, Paoli, Jean-Martin, Petkova, Violeta, Mbekhta, Mostafa, Timotin, Dan, Partington, Jonathan Richard, Elizabeth Strouse, Michel Rajoelina, Mostafa Mbekhta [Président], Dan Timotin [Rapporteur], Jonathan Richard Partington [Rapporteur], Jean-Martin Paoli, and Violeta Petkova

Subjects
Opérateurs de Toeplitz tronqués, Espace de Bergman harmonique, Espace modèle, Espace de Bergman, Opérateurs de Toeplitz

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