Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2018, Volume 146, Issue 9, pp. 4009 - 4020

In this article, we derive off-diagonal estimates of the Bergman kernel associated to tensor-powers of the cotangent line bundle defined over a hyperbolic...

Bergman kernels | MATHEMATICS | MATHEMATICS, APPLIED

Bergman kernels | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2018, Volume 146, Issue 6, pp. 2541 - 2553

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2019, Volume 371, Issue 6, pp. 4129 - 4192

Let \mathcal {X} be a complex projective manifold of dimension n defined over the reals, and let M denote its real locus. We study the vanishing locus Z_{s_d}...

real projective manifold | linear statistics | BERGMAN-KERNEL | SHUB | THEOREM | Bergman kernel | MATHEMATICS | Kac-Rice formula | SMALE | Random submanifolds | EXPANSION | SETS | Kostlan-Shub-Smale polynomials | RANDOM ZEROS | NUMBER VARIANCE | Probability | Algebraic Geometry | Mathematics | Metric Geometry

real projective manifold | linear statistics | BERGMAN-KERNEL | SHUB | THEOREM | Bergman kernel | MATHEMATICS | Kac-Rice formula | SMALE | Random submanifolds | EXPANSION | SETS | Kostlan-Shub-Smale polynomials | RANDOM ZEROS | NUMBER VARIANCE | Probability | Algebraic Geometry | Mathematics | Metric Geometry

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

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 357, Issue 2, pp. 364 - 370

In this note, we give an improvement on the Bergman kernel for the domain { ( w , z ) ∈ C m × C n : ‖ w ‖ m 2 p + ‖ z ‖ n 2 < 1 } . As an application, we...

Weighted Bergman kernel | Lu Qi-Keng problem | Bergman kernel | MATHEMATICS | MATHEMATICS, APPLIED | BERGMAN-KERNEL FUNCTION | PROJECTIONS | CONJECTURE

Weighted Bergman kernel | Lu Qi-Keng problem | Bergman kernel | MATHEMATICS | MATHEMATICS, APPLIED | BERGMAN-KERNEL FUNCTION | PROJECTIONS | CONJECTURE

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2016, Volume 68, Issue 4, pp. 1461 - 1472

We give a proof of the Ohsawa-Takegoshi extension theorem with sharp estimates. The proof is based on ideas of Blocki to use variations of domains to simplify...

Extension | Vector bundles | Bergman kernel | MATHEMATICS | extension | BERGMAN-KERNEL | RIEMANN SURFACES | HOLOMORPHIC-FUNCTIONS | vector bundles

Extension | Vector bundles | Bergman kernel | MATHEMATICS | extension | BERGMAN-KERNEL | RIEMANN SURFACES | HOLOMORPHIC-FUNCTIONS | vector bundles

Journal Article

Journal of Geometric Analysis, ISSN 1050-6926, 10/2017, Volume 27, Issue 4, pp. 2658 - 2683

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2017, Volume 86, Issue 306, pp. 1913 - 1947

We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in...

PROJECTION | CHAOS | MATHEMATICS, APPLIED | MARKOV-TYPE | POLYNOMIAL-APPROXIMATION | BERGMAN KERNELS | EQUILIBRIUM MEASURES | ASYMPTOTICS | STOCHASTIC COLLOCATION | MATHEMATICS AND COMPUTING

PROJECTION | CHAOS | MATHEMATICS, APPLIED | MARKOV-TYPE | POLYNOMIAL-APPROXIMATION | BERGMAN KERNELS | EQUILIBRIUM MEASURES | ASYMPTOTICS | STOCHASTIC COLLOCATION | MATHEMATICS AND COMPUTING

Journal Article

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9939, 11/2019, Volume 147, Issue 11, pp. 4915 - 4919

It is proved that for any domain in C-n the Caratheodory-Eisenman volume is comparable with the volume of the indicatrix of the Caratheodory metric up to...

MATHEMATICS | MATHEMATICS, APPLIED | Caratheodory metric | Bergman kernel | Caratheodory-Eisenman volume | Azukawa metric

MATHEMATICS | MATHEMATICS, APPLIED | Caratheodory metric | Bergman kernel | Caratheodory-Eisenman volume | Azukawa metric

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2014, Volume 266, Issue 5, pp. 3083 - 3133

For a weight function Q:C→R and a positive scaling parameter m, we study reproducing kernels Kq,mQ,n of the polynomial...

Determinantal point process | Polyanalytic function | Landau level | Bergman kernel | MATHEMATICS | EIGENVALUES | BERGMAN-KERNEL | THEOREM | FLUCTUATIONS | L-P SPACES | Algorithms

Determinantal point process | Polyanalytic function | Landau level | Bergman kernel | MATHEMATICS | EIGENVALUES | BERGMAN-KERNEL | THEOREM | FLUCTUATIONS | L-P SPACES | Algorithms

Journal Article

Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2016, Volume 53, Issue 5, pp. 1401 - 1409

In complex analysis, the Bergman kernels for two biholomor-phically equivalent complex domains satisfy the transformation formula. Recently new Bergman theory...

Transformation formula | Slice regular functions | Slice Bergman kernel | Quaternion variables | Bergman kernel | MATHEMATICS | transformation formula | slice regular functions | slice Bergman kernel | quaternion variables

Transformation formula | Slice regular functions | Slice Bergman kernel | Quaternion variables | Bergman kernel | MATHEMATICS | transformation formula | slice regular functions | slice Bergman kernel | quaternion variables

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2017, Volume 50, Issue 48, p. 485202

If a Hamiltonian of a quantum system is symmetric under space-time reflection, then the associated eigenvalues can be real. A conjugation operation for quantum...

superselection | Bergman kernel | hyperbolic quantum mechanics | PT symmetry | REALITY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

superselection | Bergman kernel | hyperbolic quantum mechanics | PT symmetry | REALITY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2018, Volume 457, Issue 1, pp. 233 - 247

We prove that a smooth bounded pseudoconvex domain Ω⊆C3 with a one-dimensional complex manifold M in its boundary has a noncompact ∂‾-Neumann operator on...

Compactness of the [formula omitted]-Neumann operator | Pseudoconvex domains | Bergman kernels | Compactness of the ∂‾-Neumann operator

Compactness of the [formula omitted]-Neumann operator | Pseudoconvex domains | Bergman kernels | Compactness of the ∂‾-Neumann operator

Journal Article

Journal of Geometric Analysis, ISSN 1050-6926, 04/2018, Volume 28, Issue 2, pp. 1716 - 1727

We discuss topics related to zeroes of the Bergman kernels, and present a method for generating Bergman kernels with arbitrarily, but finitely, many zeroes. It...

Bergman space | Bergman kernel | Radial weight | MATHEMATICS | SHARP ESTIMATE

Bergman space | Bergman kernel | Radial weight | MATHEMATICS | SHARP ESTIMATE

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2018, Volume 370, Issue 9, pp. 6565 - 6584

Let L be a positive line bundle over a projective complex manifold X, L^p its tensor power of order p, H^0(X,L^p) the space of holomorphic sections of L^p, and...

Equilibrium measure | Large deviations | β-ensemble | Bergman kernel | Fekete points | Bernstein-Markov property | large deviations | MATHEMATICS | equilibrium measure | beta-ensemble

Equilibrium measure | Large deviations | β-ensemble | Bergman kernel | Fekete points | Bernstein-Markov property | large deviations | MATHEMATICS | equilibrium measure | beta-ensemble

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2016, Volume 2016, Issue 16, pp. 5048 - 5075

We show that normalized currents of integration along the common zeros of random m-tuples of sections of powers of m singular Hermitian big line bundles on a...

FORMS | MATHEMATICS | ENERGY | MASS EQUIDISTRIBUTION | BERGMAN-KERNEL | THEOREM | SECTIONS | ZEROS

FORMS | MATHEMATICS | ENERGY | MASS EQUIDISTRIBUTION | BERGMAN-KERNEL | THEOREM | SECTIONS | ZEROS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2016, Volume 435, Issue 2, pp. 1426 - 1457

We study Toeplitz operator theory on the doubling Fock spaces, which are Fock spaces whose exponential weight is associated to a subharmonic function with...

Doubling measures | Schatten classes | Toeplitz operators | Fock spaces | MATHEMATICS | MATHEMATICS, APPLIED | BERGMAN-KERNEL | L-P SPACES

Doubling measures | Schatten classes | Toeplitz operators | Fock spaces | MATHEMATICS | MATHEMATICS, APPLIED | BERGMAN-KERNEL | L-P SPACES

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 12/2016, Volume 110, pp. 187 - 194

Let X be a compact connected Riemann surface of genus g, with g≥2. For each d<η(X), where η(X) is the gonality of X, the symmetric product Symd(X) embeds into...

Petersson inner product | Jacobian | Bergman kernel | Symmetric product

Petersson inner product | Jacobian | Bergman kernel | Symmetric product

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 6, pp. 1077 - 1082

Let Gi be a closed Lie subgroup of U（n）, Ωi be a bounded Gi-invariant domain in Cn which contains 0, and （9（Cn）Gi = C, for i= 1,2. If f ： f21 →2 is...

invariant domain | MATHEMATICS | MATHEMATICS, APPLIED | PROPER HOLOMORPHIC MAPPINGS | CIRCULAR DOMAINS | BERGMAN-KERNEL | biholomorphic mapping | degree of polynomial mapping | AUTOMORPHISMS | group action | Bergman kernel | STEIN-SPACES

invariant domain | MATHEMATICS | MATHEMATICS, APPLIED | PROPER HOLOMORPHIC MAPPINGS | CIRCULAR DOMAINS | BERGMAN-KERNEL | biholomorphic mapping | degree of polynomial mapping | AUTOMORPHISMS | group action | Bergman kernel | STEIN-SPACES

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2019, Volume 372, Issue 2, pp. 1113 - 1137

This work consists of two parts. In the first part, we consider a compact connected strongly pseudoconvex CR manifold X with a transversal CR S^{1} action. We...

MATHEMATICS | zero current | CR function | METRICS | Kohn Laplacian | HOLOMORPHIC SECTIONS | Szego Holomorphic function | Szego kernel | equidistribution | Bergman kernel | ZEROS

MATHEMATICS | zero current | CR function | METRICS | Kohn Laplacian | HOLOMORPHIC SECTIONS | Szego Holomorphic function | Szego kernel | equidistribution | Bergman kernel | ZEROS

Journal Article

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