Wyniki wyszukiwania

1

Operator models and Arveson's curvature invariant

100%

Engliš M.

Banach Center Publications

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2005

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tom 67

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nr 1

171-183

2

Covariant differential operators and Green's functions

72%

Engliš M., Peetre J.

Annales Polonici Mathematici

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1997

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tom 66

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nr 1

77-103

EN

The basic idea of this paper is to use the covariance of a partial differential operator under a suitable group action to determine suitable associated Green's functions. For instance, we offer a new proof of a formula for Green's function of the mth power $Δ^m$ of the ordinary Laplace's operator Δ in the unit disk 𝔻 found in a recent paper (Hayman-Korenblum, J. Anal. Math. 60 (1993), 113-133). We also study Green's functions associated with mth powers of the Poincaré invariant Laplace operator 𝜟. It turns out that they can be expressed in terms of certain special functions of which the dilogarithm (m = 2) and the trilogarithm (m = 3) are the simplest instances. Finally, we establish a relationship between $Δ^m$ and 𝜟 : the former is up to conjugation a polynomial of the latter.

3

Deformation quantization and Borel's theorem in locally convex spaces

72%

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.

4

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

59%

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.

Ograniczanie wyników

2 Studia Mathematica

1 Annales Polonici Mathematici

1 Banach Center Publications

4 Engliš M.

2 Taskinen J.

1 Bonet J.

1 Peetre J.

1 2007

2 2005

1 1997

Operator models and Arveson's curvature invariant

Covariant differential operators and Green's functions

Deformation quantization and Borel's theorem in locally convex spaces

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