Wyniki wyszukiwania

1

Toeplitz operators on Bergman spaces and Hardy multipliers

100%

Lusky W., Taskinen J.

Studia Mathematica

|

2011

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tom 204

|

nr 2

137-154

EN

We study Toeplitz operators $T_{a}$ with radial symbols in weighted Bergman spaces $A_{μ}^{p}$, 1 < p < ∞, on the disc. Using a decomposition of $A_{μ}^{p}$ into finite-dimensional subspaces the operator $T_{a}$ can be considered as a coefficient multiplier. This leads to new results on boundedness of $T_{a}$ and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of $T_{a}$ for a satisfying an assumption on the positivity of certain indefinite integrals.

2

Deformation quantization and Borel's theorem in locally convex spaces

100%

Engliš M., Taskinen J.

Studia Mathematica

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2007

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tom 180

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nr 1

77-93

EN

It is well known that one can often construct a star-product by expanding the product of two Toeplitz operators asymptotically into a series of other Toeplitz operators multiplied by increasing powers of the Planck constant h. This is the Berezin-Toeplitz quantization. We show that one can obtain in a similar way in fact any star-product which is equivalent to the Berezin-Toeplitz star-product, by using instead of Toeplitz operators other suitable mappings from compactly supported smooth functions to bounded linear operators on the corresponding Hilbert spaces. A crucial ingredient in the proof is the generalization, due to Colombeau, of the classical theorem of Borel on the existence of a function with prescribed derivatives of all orders at a point, which reduces the proof to a construction of a locally convex space enjoying some special properties.

3

Weighted $L^{∞}$-estimates for Bergman projections

81%

Bonet J., Engliš M., Taskinen J.

Studia Mathematica

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2005

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tom 171

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nr 1

67-92

EN

We consider Bergman projections and some new generalizations of them on weighted $L^{∞}(𝔻)$-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.

4

Associated weights and spaces of holomorphic functions

81%

Bierstedt K. D., Bonet J., Taskinen J.

Studia Mathematica

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1998

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tom 127

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nr 2

137-168

EN

When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset $G ⊂ ℂ^N$ which play an important role in the projective description problem. A number of relevant examples are provided, and a "new projective description problem" is posed. The proof of our main result can also serve to characterize when the embedding of two weighted Banach spaces of holomorphic functions is compact. Our investigations on conditions when an associated weight coincides with the original one and our estimates of the associated weights in several cases (mainly for G = ℂ or D) should be of independent interest.

5

The projective tensor product of Fréchet-Montel spaces

50%

Taskinen J.

Studia Mathematica

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1988

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tom 91

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nr 1

17-30

Ograniczanie wyników

5 Studia Mathematica

5 Taskinen J.

2 Bonet J.

2 Engliš M.

1 Bierstedt K. D.

1 Lusky W.

1 2011

1 2007

1 2005

1 1998

1 1988

Toeplitz operators on Bergman spaces and Hardy multipliers

Deformation quantization and Borel's theorem in locally convex spaces

Weighted $L^{∞}$-estimates for Bergman projections

Associated weights and spaces of holomorphic functions

The projective tensor product of Fréchet-Montel spaces