Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, pp. 1434 - 1462

We extend the classical theory of Qp-spaces of Aulaskari, Xiao and Zhao in two directions: first, by considering more general construction of such spaces; and...

Möbius invariance | [formula omitted]-spaces | Bloch space

Möbius invariance | [formula omitted]-spaces | Bloch space

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, pp. 1434 - 1462

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, p. 1434

We extend the classical theory of Q.sub.p-spaces of Aulaskari, Xiao and Zhao in two directions: first, by considering more general construction of such spaces;...

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2015, Volume 429, Issue 1, pp. 233 - 272

We give a complete description of the boundary behaviour of the Poisson kernel and the harmonic Bergman kernel of a bounded domain with smooth boundary, which...

Poisson kernel | Harmonic Bergman kernel | Pseudodifferential boundary operators | MATHEMATICS | MATHEMATICS, APPLIED | SPACES

Poisson kernel | Harmonic Bergman kernel | Pseudodifferential boundary operators | MATHEMATICS | MATHEMATICS, APPLIED | SPACES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 347, pp. 780 - 826

We study the complex geometry of generalized Kepler manifolds, defined in Jordan theoretic terms, introduce Hilbert spaces of holomorphic functions defined by...

Symmetric domain | Reproducing kernel | Asymptotic expansion | Normal algebraic variety | MATHEMATICS | BALL | TOEPLITZ-OPERATORS | HANKEL-OPERATORS

Symmetric domain | Reproducing kernel | Asymptotic expansion | Normal algebraic variety | MATHEMATICS | BALL | TOEPLITZ-OPERATORS | HANKEL-OPERATORS

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 03/2019, Volume 64, Issue 3, pp. 519 - 540

We show that the usual Poincaré metric is the only radial balanced metric on the disc with not too wild boundary behaviour. Additionally, we identify...

32Q15 | 32A36 | 53C55 | Balanced metric | strictly pseudoconvex domain | Bergman kernel | 30F45 | MATHEMATICS | SCALAR CURVATURE

32Q15 | 32A36 | 53C55 | Balanced metric | strictly pseudoconvex domain | Bergman kernel | 30F45 | MATHEMATICS | SCALAR CURVATURE

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 09/2016, Volume 271, Issue 5, pp. 1243 - 1261

For weights ρ which are either radial on the unit ball or depend only on the vertical coordinate on the upper half-space, we describe the asymptotic behaviour...

Asymptotic expansion | Bergman kernel | Harmonic Bergman kernel | MATHEMATICS | BALL | BEREZIN TRANSFORM | UNIT | REPRODUCING KERNELS | SPACES | THEOREM | QUANTIZATION

Asymptotic expansion | Bergman kernel | Harmonic Bergman kernel | MATHEMATICS | BALL | BEREZIN TRANSFORM | UNIT | REPRODUCING KERNELS | SPACES | THEOREM | QUANTIZATION

Journal Article

Advances in Mathematics, ISSN 0001-8708, 06/2015, Volume 278, p. 254

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 367, Issue 1, pp. 75 - 97

We show that the Berezin transform associated to the harmonic Fock (Segal–Bargmann) space on C n has an asymptotic expansion analogously as in the holomorphic...

Berezin transform | Harmonic Bergman kernel | Asymptotic expansion | Horn hypergeometric functions | Harmonic Fock space | MATHEMATICS | MATHEMATICS, APPLIED | UNIT | TOEPLITZ QUANTIZATION | OPERATORS | BERGMAN SPACES | KERNELS | Universities and colleges

Berezin transform | Harmonic Bergman kernel | Asymptotic expansion | Horn hypergeometric functions | Harmonic Fock space | MATHEMATICS | MATHEMATICS, APPLIED | UNIT | TOEPLITZ QUANTIZATION | OPERATORS | BERGMAN SPACES | KERNELS | Universities and colleges

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 12/2015, Volume 60, Issue 12, pp. 1712 - 1726

We obtain a formula for the Sobolev inner product in standard weighted Bergman spaces of holomorphic functions on a bounded symmetric domain in terms of the...

Bergman space | Primary: 32M15 | Secondary: 32A36 | 46E35 | bounded symmetric domain | Sobolev space | MATHEMATICS | RECURRENCE FORMULAS | OPERATORS | Eulers equations | Mathematical analysis | Decomposition | Complex variables | Formulas (mathematics) | Standards | Symmetry

Bergman space | Primary: 32M15 | Secondary: 32A36 | 46E35 | bounded symmetric domain | Sobolev space | MATHEMATICS | RECURRENCE FORMULAS | OPERATORS | Eulers equations | Mathematical analysis | Decomposition | Complex variables | Formulas (mathematics) | Standards | Symmetry

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 05/2005, Volume 17, Issue 4, pp. 391 - 490

This survey is an overview of some of the better known quantization techniques (for systems with finite numbers of degrees-of-freedom) including in particular...

Berezin quantization | Bereziu Touplitz quantization | Deformation quantization | Geometric quantization | Coherent state quantization | Canonical quantization | Borel quantization | borel quantization | canonical quantization | GEOMETRIC-QUANTIZATION | DIFFEOMORPHISM-GROUPS | PHYSICS, MATHEMATICAL | ORDERING PROBLEM | Berezin-Toeplitz quantization | QUANTUM RIEMANN SURFACES | COHERENT-STATE REPRESENTATIONS | deformation quantization | HARMONIC-ANALYSIS | coherent state quantization | TOEPLITZ QUANTIZATION | PHASE-SPACE REDUCTION | geometric quantization | Physicists | Methods

Berezin quantization | Bereziu Touplitz quantization | Deformation quantization | Geometric quantization | Coherent state quantization | Canonical quantization | Borel quantization | borel quantization | canonical quantization | GEOMETRIC-QUANTIZATION | DIFFEOMORPHISM-GROUPS | PHYSICS, MATHEMATICAL | ORDERING PROBLEM | Berezin-Toeplitz quantization | QUANTUM RIEMANN SURFACES | COHERENT-STATE REPRESENTATIONS | deformation quantization | HARMONIC-ANALYSIS | coherent state quantization | TOEPLITZ QUANTIZATION | PHASE-SPACE REDUCTION | geometric quantization | Physicists | Methods

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2008, Volume 255, Issue 6, pp. 1419 - 1457

For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a...

Toeplitz operator | Pseudodifferential operator | Sobolev space | Bergman kernel | MATHEMATICS | pseudodifferential operator | PSEUDOCONVEX DOMAINS | BIHOLOMORPHIC-MAPPINGS | HOLOMORPHIC-FUNCTIONS | COMPLEX POWERS | PROJECTIONS | ELLIPTIC PSEUDODIFFERENTIAL-OPERATORS | BOUNDARY-BEHAVIOR

Toeplitz operator | Pseudodifferential operator | Sobolev space | Bergman kernel | MATHEMATICS | pseudodifferential operator | PSEUDOCONVEX DOMAINS | BIHOLOMORPHIC-MAPPINGS | HOLOMORPHIC-FUNCTIONS | COMPLEX POWERS | PROJECTIONS | ELLIPTIC PSEUDODIFFERENTIAL-OPERATORS | BOUNDARY-BEHAVIOR

Journal Article

Operator Theory: Advances and Applications, ISSN 0255-0156, 2016, Volume 251, pp. 69 - 115

Journal Article

Advances in Mathematics, ISSN 0001-8708, 06/2015, Volume 278, pp. 254 - 254

Journal Article

Acta Mathematica Sinica, English Series, ISSN 1439-8516, 8/2018, Volume 34, Issue 8, pp. 1297 - 1312

It was conjectured by the first author and Peetre that the higher Laplace–Beltrami operators generate the whole ring of invariant operators on bounded...

Bergman Kernel | 32A25 | 32M15 | Higher Laplace–Beltrami operators | bounded symmetric domains | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | BEREZIN TRANSFORM | REPRODUCING KERNELS | SPACES | Higher Laplace-Beltrami operators | ASYMPTOTIC-EXPANSION | INVARIANT DIFFERENTIAL-OPERATORS | QUANTIZATION | Operators | Asymptotic series | Laplace transforms | Mathematical analysis | Curvature | Rings (mathematics)

Bergman Kernel | 32A25 | 32M15 | Higher Laplace–Beltrami operators | bounded symmetric domains | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | BEREZIN TRANSFORM | REPRODUCING KERNELS | SPACES | Higher Laplace-Beltrami operators | ASYMPTOTIC-EXPANSION | INVARIANT DIFFERENTIAL-OPERATORS | QUANTIZATION | Operators | Asymptotic series | Laplace transforms | Mathematical analysis | Curvature | Rings (mathematics)

Journal Article

Advances in Mathematics, ISSN 0001-8708, 04/2015, Volume 274, pp. 606 - 630

We prove the Arveson–Douglas essential normality conjecture for graded Hilbert submodules that consist of functions vanishing on a given homogeneous subvariety...

Generalized Toeplitz operator | Arveson–Douglas conjecture | Secondary | Primary | Arveson-Douglas conjecture | MATHEMATICS | PSEUDOCONVEX DOMAINS | WEIGHTED BERGMAN KERNELS | TOEPLITZ-OPERATORS | SUBMODULES | ESSENTIAL NORMALITY

Generalized Toeplitz operator | Arveson–Douglas conjecture | Secondary | Primary | Arveson-Douglas conjecture | MATHEMATICS | PSEUDOCONVEX DOMAINS | WEIGHTED BERGMAN KERNELS | TOEPLITZ-OPERATORS | SUBMODULES | ESSENTIAL NORMALITY

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 07/2016, Volume 271, Issue 2, pp. 264 - 288

For a class of O(n+1,R) invariant measures on the Kepler manifold possessing finite moments of all orders, we describe the reproducing kernels of the...

Tian–Yau–Zelditch expansion | Bergman kernel | Kepler manifold | Balanced metric | Tian-Yau-Zelditch expansion | KAHLER-MANIFOLDS | SPACES | THEOREM | VARIETIES | SCALAR CURVATURE | MATHEMATICS | PROJECTION | MINIMAL BALL | QUANTIZATION | Mathematics

Tian–Yau–Zelditch expansion | Bergman kernel | Kepler manifold | Balanced metric | Tian-Yau-Zelditch expansion | KAHLER-MANIFOLDS | SPACES | THEOREM | VARIETIES | SCALAR CURVATURE | MATHEMATICS | PROJECTION | MINIMAL BALL | QUANTIZATION | Mathematics

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2009, Volume 361, Issue 2, pp. 1039 - 1052

We show that for any localization operator on the Fock space with polynomial window, there exists a constant coefficient linear partial differential operator D...

Partial differential operators | Differential operators | Topological theorems | Constant coefficients | Linear transformations | Fourier transformations | Polynomials | Operator theory | Symmetry | Bounded symmetric domain | Localization operator | Toeplitz operator | Segal-bargmann space | Bergman space? | Bergman space | MATHEMATICS | localization operator | bounded symmetric domain | Segal-Bargmann space

Partial differential operators | Differential operators | Topological theorems | Constant coefficients | Linear transformations | Fourier transformations | Polynomials | Operator theory | Symmetry | Bounded symmetric domain | Localization operator | Toeplitz operator | Segal-bargmann space | Bergman space? | Bergman space | MATHEMATICS | localization operator | bounded symmetric domain | Segal-Bargmann space

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2012, Volume 389, Issue 2, pp. 1086 - 1104

We give criteria for boundedness of the associated Bergman-type projections on Lp spaces on Cn with respect to generalized Gaussian weights exp(−|z|2m), m>0....

Reproducing kernel | Higher order Fock space | Bergman projection | Mittag–Leffler function | Mittag-Leffler function | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL ASYMPTOTICS | OPERATORS

Reproducing kernel | Higher order Fock space | Bergman projection | Mittag–Leffler function | Mittag-Leffler function | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL ASYMPTOTICS | OPERATORS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2009, Volume 361, Issue 3, pp. 1173 - 1188

We show that, perhaps surprisingly, in several aspects the behaviour of the reproducing kernels of Toeplitz operators and of the Berezin transform on some...

Unit ball | Mathematical theorems | Differential operators | Analytic functions | Steepest descent method | Mathematical functions | Mathematics | Polynomials | Complex variables | Rotation | Berezin transform | Pluriharmonic Bergman kernel | pluriharmonic Bergman kernel | MATHEMATICS | TOEPLITZ QUANTIZATION | DOMAINS | KERNELS

Unit ball | Mathematical theorems | Differential operators | Analytic functions | Steepest descent method | Mathematical functions | Mathematics | Polynomials | Complex variables | Rotation | Berezin transform | Pluriharmonic Bergman kernel | pluriharmonic Bergman kernel | MATHEMATICS | TOEPLITZ QUANTIZATION | DOMAINS | KERNELS

Journal Article

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