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## Search Articles

2012, 2012, Graduate Texts in Mathematics, ISBN 9781441988003, Volume 263, 350

While Hardy and Bergman spaces are established subjects in the literature on analytic functions, Fock spaces remain virgin territory...

Functional analysis | Operator theory | Functions of complex variables | Several Complex Variables and Analytic Spaces | Operator Theory | Mathematics | Functional Analysis | Mathematics and Statistics | Functions of a Complex Variable | Analytic spaces | Functions of several complex variables

Functional analysis | Operator theory | Functions of complex variables | Several Complex Variables and Analytic Spaces | Operator Theory | Mathematics | Functional Analysis | Mathematics and Statistics | Functions of a Complex Variable | Analytic spaces | Functions of several complex variables

eBook

Journal of inequalities and applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 10

...)$
be the Fock space induced by ϕ. In this paper, we conclude that the Bergman projection is bounded from the pth Lebesgue space
L
p
(
ϕ
)
$L^{p}(\phi )$
to
F
p
(
ϕ
)
$\mathcal{F}^{p}(\phi)$
for
1
≤
p
≤
∞
$1\leq p \leq\infty...

reverse-Hölder inequality | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Bergman projection | Bergman kernel | Physical Sciences | Mathematics, Applied | Science & Technology | Eigenvalues | Mathematical analysis | Complex variables | Research

reverse-Hölder inequality | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Bergman projection | Bergman kernel | Physical Sciences | Mathematics, Applied | Science & Technology | Eigenvalues | Mathematical analysis | Complex variables | Research

Journal Article

The Journal of geometric analysis, ISSN 1559-002X, 05/2011, Volume 23, Issue 1, pp. 170 - 201

Hankel operators with anti-holomorphic symbols are studied for a large class of weighted Fock spaces on ℂ
n...

32A37 | Fock space | 32A36 | Mathematics | Bergman kernel | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | 47B35 | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Hankel operator | Physical Sciences | Science & Technology

32A37 | Fock space | 32A36 | Mathematics | Bergman kernel | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | 47B35 | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Hankel operator | Physical Sciences | Science & Technology

Journal Article

2016, Volume 679

General theory of linear operators | Other Dirichlet series and zeta functions | Completeness of eigenfunctions, eigenfunction expansions | Analytic functions | Functions of a complex variable | Partial differential equations | Spaces and algebras of analytic functions | Cyclic vectors, hypercyclic and chaotic operators | Bounded analytic functions | Spectral theory and eigenvalue problems | Operator theory | Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) | Special classes of linear operators | Bergman spaces, Fock spaces | Analytic spaces | Zeta and $L$-functions: analytic theory | Number theory

Conference Proceeding

The Rocky Mountain journal of mathematics, ISSN 0035-7596, 2019, Volume 49, Issue 1, pp. 47 - 71

We discuss the regularity of extremal functions in certain weighted Bergman and Fock type spaces...

Bergman space | Density of polynomials | And phrases. Extremal problem | Fock space | Regularity | Physical Sciences | Mathematics | Science & Technology

Bergman space | Density of polynomials | And phrases. Extremal problem | Fock space | Regularity | Physical Sciences | Mathematics | Science & Technology

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 case...

Berezin transform | Harmonic Bergman kernel | Asymptotic expansion | Horn hypergeometric functions | Harmonic Fock space | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Universities and colleges

Berezin transform | Harmonic Bergman kernel | Asymptotic expansion | Horn hypergeometric functions | Harmonic Fock space | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Universities and colleges

Journal Article

Communications in contemporary mathematics, ISSN 0219-1997, 10/2014, Volume 16, Issue 5, pp. 1350034 - 1-1350034-49

... of ℂN as weighted symmetric Fock spaces over ℂN. We develop the basics of operator theory on these spaces related to shift operators...

extension | analytic Hilbert module | radial differential operator | Toeplitz | multiplier | shift | virtual point | Bergman | Hardy | short exact sequence | Drury-Arveson | Fock | von Neumann inequality | Busby invariant | spectrum | Fredholm | subnormal | K-groups | Dirichlet | reproducing kernel Hilbert space | commutant | C∗-algebra | hyponormal | row contraction | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Operators (mathematics) | Analytic functions | Mathematical analysis | Differential equations | Dirichlet problem | Hilbert space | Normality | Weight | Functions (mathematics) | Operators | Algebra | Inequalities | Multivariable | Touch

extension | analytic Hilbert module | radial differential operator | Toeplitz | multiplier | shift | virtual point | Bergman | Hardy | short exact sequence | Drury-Arveson | Fock | von Neumann inequality | Busby invariant | spectrum | Fredholm | subnormal | K-groups | Dirichlet | reproducing kernel Hilbert space | commutant | C∗-algebra | hyponormal | row contraction | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Operators (mathematics) | Analytic functions | Mathematical analysis | Differential equations | Dirichlet problem | Hilbert space | Normality | Weight | Functions (mathematics) | Operators | Algebra | Inequalities | Multivariable | Touch

Journal Article

Annals of global analysis and geometry, ISSN 0232-704X, 6/2016, Volume 49, Issue 4, pp. 349 - 359

The Fock–Bargmann–Hartogs domain
$$D_{n,m}(\mu )$$
D
n
,
m
(
μ
)
(
$$\mu >0$$
μ
>
0
) in
$$\mathbb {C}^{n+m}$$
C
n
+
m
is defined by the inequality...

32A25 | Balanced metrics | Theoretical, Mathematical and Computational Physics | Mathematics | Bergman kernels | Kähler metrics | Geometry | 32Q15 | Fock–Bargmann–Hartogs domains | 32M15 | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Group Theory and Generalizations | Physical Sciences | Science & Technology | Studies | Mathematical models | Kernels | Texts | Hilbert space | Mathematical analysis | Inequalities

32A25 | Balanced metrics | Theoretical, Mathematical and Computational Physics | Mathematics | Bergman kernels | Kähler metrics | Geometry | 32Q15 | Fock–Bargmann–Hartogs domains | 32M15 | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Group Theory and Generalizations | Physical Sciences | Science & Technology | Studies | Mathematical models | Kernels | Texts | Hilbert space | Mathematical analysis | Inequalities

Journal Article

The Journal of geometric analysis, ISSN 1050-6926, 2009, Volume 19, Issue 4, pp. 890 - 910

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in L (2)(e (-2 phi...

Bergman kernel | Compactness canonical operator | Physical Sciences | Mathematics | Science & Technology | Mathematics - Complex Variables | Holomorphic functions | Functions of complex variables | Funcions holomorfes | Funcions de variables complexes

Bergman kernel | Compactness canonical operator | Physical Sciences | Mathematics | Science & Technology | Mathematics - Complex Variables | Holomorphic functions | Functions of complex variables | Funcions holomorfes | Funcions de variables complexes

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2018, Volume 68, Issue 6, pp. 2311 - 2328

We show that under mild conditions, a Gaussian analytic function F that a.s. does not belong to a given weighted Bergman space or Bargmann- Fock space has the property that a.s...

Fock | Bargmann | Bergman | Gaussian | Random | Physical Sciences | Mathematics | Science & Technology

Fock | Bargmann | Bergman | Gaussian | Random | Physical Sciences | Mathematics | Science & Technology

Journal Article

Journal of functional analysis, ISSN 0022-1236, 11/2019, Volume 277, Issue 10, pp. 3436 - 3466

.... In this paper, we study weighted composition operators acting between two large weighted Fock spaces Fωp and Fωq...

Bergman space | Carleson measure | Weighted composition operators | Schatten class | Physical Sciences | Mathematics | Science & Technology

Bergman space | Carleson measure | Weighted composition operators | Schatten class | Physical Sciences | Mathematics | Science & Technology

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 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Reproducing kernel | Higher order Fock space | Bergman projection | Mittag–Leffler function | Mittag-Leffler function | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Indiana University mathematics journal, ISSN 0022-2518, 1/2015, Volume 64, Issue 5, pp. 1553 - 1573

In this paper, we study the compactness of operators on the Bergman space of the unit ball and on very generally weighted Bargmann-Fock spaces in terms of the behavior of their Berezin transforms...

Bergman space | Berezin transform | Compact operators | Sufficiently localized operator | Toeplitz operator | Fock space | Physical Sciences | Mathematics | Science & Technology

Bergman space | Berezin transform | Compact operators | Sufficiently localized operator | Toeplitz operator | Fock space | Physical Sciences | Mathematics | Science & Technology

Journal Article

Journal of the Australian Mathematical Society (2001), ISSN 1446-7887, 02/2015, Volume 98, Issue 1, pp. 129 - 144

... ${\rm\Lambda}_{t}$ with $t>1$. We also obtain a version for Bergman and Fock spaces.

atomic decomposition | Berezin transform | Lipschitz spaces | Bergman spaces | Carleson measures | Besov spaces | Fock spaces | Physical Sciences | Mathematics | Science & Technology | Mathematics - Complex Variables

atomic decomposition | Berezin transform | Lipschitz spaces | Bergman spaces | Carleson measures | Besov spaces | Fock spaces | Physical Sciences | Mathematics | Science & Technology | Mathematics - Complex Variables

Journal Article

Journal of functional analysis, ISSN 0022-1236, 06/2015, Volume 268, Issue 12, pp. 3790 - 3833

.... The asymptotic analysis we give is in the setting of the holomorphic and the harmonic Fock spaces, respectively.

Bergman space | Berezin transform | Asymptotic analysis | Harmonic Fock space | Physical Sciences | Mathematics | Science & Technology

Bergman space | Berezin transform | Asymptotic analysis | Harmonic Fock space | Physical Sciences | Mathematics | Science & Technology

Journal Article

Complex analysis and operator theory, ISSN 1661-8262, 09/2019, Volume 13, Issue 7, pp. 3457 - 3478

.... In particular, weighted Bergman and Fock type spaces of polyanalytic functions are introduced...

Bergman space | Reproducing kernel | Operator Theory | Primary 32A23 | Fock space | 32A36 | Polyanalytic function | Analysis | Mathematics, general | Mathematics | 30A94 | Physical Sciences | Mathematics, Applied | Science & Technology | Kernels | Analytic functions | Mathematical analysis | Hilbert space | Polynomials | Rotation | Invariants

Bergman space | Reproducing kernel | Operator Theory | Primary 32A23 | Fock space | 32A36 | Polyanalytic function | Analysis | Mathematics, general | Mathematics | 30A94 | Physical Sciences | Mathematics, Applied | Science & Technology | Kernels | Analytic functions | Mathematical analysis | Hilbert space | Polynomials | Rotation | Invariants

Journal Article

Integral equations and operator theory, ISSN 0378-620X, 11/2013, Volume 77, Issue 3, pp. 355 - 370

We obtain sufficient conditions for a densely-defined operator on the Fock space to be bounded or compact...

47B07 | Bergman space | 47B38 | Fock space | Gaussian measure | Analysis | Secondary 47B35 | Berezin transform | Hilbert–Schmidt operator | Mathematics | Toeplitz operator | Primary 30H20 | Hilbert-Schmidt operator | Physical Sciences | Science & Technology

47B07 | Bergman space | 47B38 | Fock space | Gaussian measure | Analysis | Secondary 47B35 | Berezin transform | Hilbert–Schmidt operator | Mathematics | Toeplitz operator | Primary 30H20 | Hilbert-Schmidt operator | Physical Sciences | Science & Technology

Journal Article

18.
Full Text
Asymptotic Expansion of the Bergman Kernel via Perturbation of the Bargmann–Fock Model

The Journal of geometric analysis, ISSN 1050-6926, 10/2016, Volume 26, Issue 4, pp. 2602 - 2638

.... We use the observation that after rescaling the Kahler potential in a -neighborhood of a given point, the potential becomes an asymptotic perturbation of the Bargmann-Fock metric...

Asymptotic expansion | Bargmann–Fock space | Bergman kernel | Kahler manifolds | Physical Sciences | Mathematics | Science & Technology | Kernels

Asymptotic expansion | Bargmann–Fock space | Bergman kernel | Kahler manifolds | Physical Sciences | Mathematics | Science & Technology | Kernels

Journal Article

Complex variables and elliptic equations, ISSN 1747-6933, 04/2016, Volume 61, Issue 4, pp. 562 - 573

In this paper, we define a class of integral operators on the space
associated with the Fock space...

integral operators | Fock spaces | Bergman spaces | Physical Sciences | Mathematics | Science & Technology | Norms | Operators | Complex variables | Integrals | Mathematical analysis | Images

integral operators | Fock spaces | Bergman spaces | Physical Sciences | Mathematics | Science & Technology | Norms | Operators | Complex variables | Integrals | Mathematical analysis | Images

Journal Article

Complex variables and elliptic equations, ISSN 1747-6933, 09/2020

...(2)} be the Fock-Bargmann-Hartogs domain, where mu > 0. For any fixed positive integer m, we prove that there exists a unique positive integer n(0...

Physical Sciences | Mathematics | Science & Technology

Physical Sciences | Mathematics | Science & Technology

Journal Article

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