Berezin transforms and group representations.

Nomura, Takaaki

Displaying similar documents to “Berezin transforms and group representations.”

Two-parametric liftings of Toeplitz forms.

Pedro Alegría Ezquerra (1992)

Extracta Mathematicae

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The parametrization problem of the minimal unitary extensions of an isometric operator allows its application, through the spectral theorem, to the case of the Fourier representations of a bounded Hankel form with respect to the norms (∫ |f|dμ) and (∫ |f|dμ) where μ, μ are positive finite measures in T~[0,2π[ (see [1]). In this work we develop a similar procedure for the two-parametric case, where μ, μ are positive measures defined in T~[0,2π[x[0,2π[. With this purpose, we define the...

Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices

A.K. Abdikalykov, V.N. Chugunov, Kh.D. Ikramov (2015)

Special Matrices

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Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.

On Pták’s generalization of Hankel operators

Carmen H. Mancera, Pedro José Paúl (2001)

Czechoslovak Mathematical Journal

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In 1997 Pták defined generalized Hankel operators as follows: Given two contractions $T_{1} \in ℬ (ℋ_{1})$ and $T_{2} \in ℬ (ℋ_{2})$ , an operator $X ℋ_{1} \to ℋ_{2}$ is said to be a generalized Hankel operator if $T_{2} X = X T_{1}^{*}$ and $X$ satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of $T_{1}$ and $T_{2}$ . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong...

Unitary parts of generalized Hankel operators

Jeffrey R. Butz (1978)

Colloquium Mathematicae

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Operators of Hankel type

S. Bermudo, S. A. M. Marcantognini, M. D. Morán (2006)

Czechoslovak Mathematical Journal

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Hankel operators and their symbols, as generalized by V. Pták and P. Vrbová, are considered. The present note provides a parametric labeling of all the Hankel symbols of a given Hankel operator $X$ by means of Schur class functions. The result includes uniqueness criteria and a Schur like formula. As a by-product, a new proof of the existence of Hankel symbols is obtained. The proof is established by associating to the data of the problem a suitable isometry $V$ so that there is a bijective...

Properties of non-unitary zero mass induced representations of the Poincaré group on the space of tensor-valued functions

A. O. Barut, R. Raczka (1972)

Annales de l'I.H.P. Physique théorique

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Berezin quantization and holomorphic representations

Benjamin Cahen (2013)

Rendiconti del Seminario Matematico della Università di Padova

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The Berezin transform and operators on spaces of analytic functions

Karel Stroethoff (1997)

Banach Center Publications

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In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz...