1971, Lecture notes in mathematics, ISBN 9780387057026, Volume 241., iv, 89

Book

1980, Kanô memorial lectures, ISBN 9780691082714, Volume 4, xvi, 321

Book

1992, Translations of mathematical monographs, ISBN 9780821845660, Volume 111., v, 132

Book

International Journal of Mathematics, ISSN 0129-167X, 07/2018, Volume 29, Issue 8, p. 1850057

In this paper, we characterize the Hartogs domains over homogeneous Siegel domains of type II and explicitly describe their automorphism groups. Moreover, we...

proper holomorphic map | Hartogs domain | Biholomorphism | homogeneous Siegel domain | MATHEMATICS | MAPPINGS | HOLOMORPHIC AUTOMORPHISM GROUP

proper holomorphic map | Hartogs domain | Biholomorphism | homogeneous Siegel domain | MATHEMATICS | MAPPINGS | HOLOMORPHIC AUTOMORPHISM GROUP

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 4/2017, Volume 27, Issue 2, pp. 1703 - 1736

We obtain an explicit formula of the Bergman kernel for Hartogs domains over bounded homogeneous domains. In order to find a simple formula, we consider a...

Primary 32A25 | Bounded homogeneous domains | Normal j-algebra | Mathematics | 32M10 | Bergman kernel | 32A07 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Hartogs domains | Differential Geometry | Dynamical Systems and Ergodic Theory | Siegel domain | REPRESENTATIONS | SIEGEL DOMAINS | CLASSIFICATION | SYMMETRIC DOMAINS | MATHEMATICS | COMPLEX ELLIPSOIDS | CURVATURE | EXPLICIT FORMULAS | ZEROS | Algebra | Research institutes

Primary 32A25 | Bounded homogeneous domains | Normal j-algebra | Mathematics | 32M10 | Bergman kernel | 32A07 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Hartogs domains | Differential Geometry | Dynamical Systems and Ergodic Theory | Siegel domain | REPRESENTATIONS | SIEGEL DOMAINS | CLASSIFICATION | SYMMETRIC DOMAINS | MATHEMATICS | COMPLEX ELLIPSOIDS | CURVATURE | EXPLICIT FORMULAS | ZEROS | Algebra | Research institutes

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 04/2019, Volume 199, Issue 1, pp. 291 - 306

The purpose of this paper is to calculate explicitly the volumes of Siegel sets which are coarse fundamental domains for the action of SL .sub.n ( Z) SL n ( Z...

Volumes | Arithmetic groups | Coarse fundamental domains | Siegel sets

Volumes | Arithmetic groups | Coarse fundamental domains | Siegel sets

Journal Article

Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, ISSN 0025-5858, 10/2018, Volume 88, Issue 2, pp. 273 - 288

We discuss generalizations of classical theta series, requiring only some basic properties of the classical setting. As it turns out, the existence of a...

Theta series | Convex cone | Jordan algebra | Siegel domain | MATHEMATICS | AUTOMORPHISMS | Algebra | Mathematics - Complex Variables

Theta series | Convex cone | Jordan algebra | Siegel domain | MATHEMATICS | AUTOMORPHISMS | Algebra | Mathematics - Complex Variables

Journal Article

2014, Memoirs of the American Mathematical Society, ISBN 9780821898567, Volume no. 1090., v, 107

Book

Geometriae Dedicata, ISSN 0046-5755, 12/2012, Volume 161, Issue 1, pp. 119 - 128

We prove that a homogeneous bounded domain admits a Berezin quantization.

Geometry | Berezin quantization | 53C55 | Bounded homogeneous domain | 53D05 | Mathematics | 58F06 | Calabi’s diastasis function | Kähler metrics | Calabi's diastasis function | KAHLER-MANIFOLDS | MATHEMATICS | REPRESENTATIONS | SIEGEL DOMAINS | EXPANSION | METRICS | VARIETIES | SCALAR CURVATURE | Kahler metrics

Geometry | Berezin quantization | 53C55 | Bounded homogeneous domain | 53D05 | Mathematics | 58F06 | Calabi’s diastasis function | Kähler metrics | Calabi's diastasis function | KAHLER-MANIFOLDS | MATHEMATICS | REPRESENTATIONS | SIEGEL DOMAINS | EXPANSION | METRICS | VARIETIES | SCALAR CURVATURE | Kahler metrics

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 11/2012, Volume 24, Issue 10, p. 1250024

We determine the homogeneous Kähler diffeomorphism FC which expresses the Kähler two-form on the Siegel–Jacobi ball ${\mathcal D}^J_n = {\mathbb C}^n\times...

Jacobi group | coherent and squeezed states | Berezin quantization | Siegel-Jacobi domains | fundamental conjecture for homogeneous Kähler manifolds | matrix Riccati equation | REPRESENTATIONS | FIELD | COHERENT STATES | PHYSICS, MATHEMATICAL | OSCILLATOR | FORMS | SPACE | MECHANICS | fundamental conjecture for homogeneous Kahler manifolds | MANIFOLDS | QUANTIZATION

Jacobi group | coherent and squeezed states | Berezin quantization | Siegel-Jacobi domains | fundamental conjecture for homogeneous Kähler manifolds | matrix Riccati equation | REPRESENTATIONS | FIELD | COHERENT STATES | PHYSICS, MATHEMATICAL | OSCILLATOR | FORMS | SPACE | MECHANICS | fundamental conjecture for homogeneous Kahler manifolds | MANIFOLDS | QUANTIZATION

Journal Article

GEOMETRIAE DEDICATA, ISSN 0046-5755, 04/2019, Volume 199, Issue 1, pp. 291 - 306

The purpose of this paper is to calculate explicitly the volumes of Siegel sets which are coarse fundamental domains for the action of SLn(Z) in SLn(R), so...

MATHEMATICS | Volumes | Arithmetic groups | Siegel sets | Coarse fundamental domains

MATHEMATICS | Volumes | Arithmetic groups | Siegel sets | Coarse fundamental domains

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 12/2011, Volume 8, Issue 8, pp. 1783 - 1798

We study the holomorphic unitary representations of the Jacobi group based on Siegel-Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces...

Siegel-Jacobi domain | Jacobi group | Fock representation | scalar holomorphic discrete series | canonical automorphy factor | canonical kernel function | COHERENT STATES | PHYSICS, MATHEMATICAL | FORMS | SPACE | FOCK REPRESENTATIONS | LIE-GROUPS | TRANSFORM | Disks | Scalars | Construction | Representations | Space based | Mathematical analysis

Siegel-Jacobi domain | Jacobi group | Fock representation | scalar holomorphic discrete series | canonical automorphy factor | canonical kernel function | COHERENT STATES | PHYSICS, MATHEMATICAL | FORMS | SPACE | FOCK REPRESENTATIONS | LIE-GROUPS | TRANSFORM | Disks | Scalars | Construction | Representations | Space based | Mathematical analysis

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 09/2017, Volume 62, Issue 9, pp. 1192 - 1203

The goal of this note is to explore the relationship between the Folland-Kohn basic estimate and the Z(q)-condition. In particular, on unbounded domains, we...

Heisenberg group | strictly pseudoconvex | Siegel upper half space | 35N15 | uniform Z(q) | closed range of | Primary: 32W05 | Z(q) | unbounded domain | Secondary: 32W10 | 32T15 | Equivalence | Estimates

Heisenberg group | strictly pseudoconvex | Siegel upper half space | 35N15 | uniform Z(q) | closed range of | Primary: 32W05 | Z(q) | unbounded domain | Secondary: 32W10 | 32T15 | Equivalence | Estimates

Journal Article

Results in Mathematics, ISSN 1422-6383, 12/2019, Volume 74, Issue 4, pp. 1 - 24

The Siegel domain in the space $$C^n$$ Cn is defined as follows: $$\begin{aligned} \Omega _n=\left\{ \eta =(\eta _1,\eta _2,\dots ,\eta _n)\in C^n: Im \eta...

32A26 | 32A25 | 32A36 | 30E20 | weighted integral representations | Mathematics | conjugate pluriharmonic functions | holomorphic and pluriharmonic functions | 30H20 | 32A07 | 30H10 | weighted function spaces | Mathematics, general | Siegel domain

32A26 | 32A25 | 32A36 | 30E20 | weighted integral representations | Mathematics | conjugate pluriharmonic functions | holomorphic and pluriharmonic functions | 30H20 | 32A07 | 30H10 | weighted function spaces | Mathematics, general | Siegel domain

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2003, Volume 41, Issue 3, pp. 932 - 953

We extend the method of Kazantzis and Kravaris [Systems Control Lett., 34 (1998), pp. 241 247] for the design of an observer to a larger class of nonlinear...

Siegel's theorem | Lyapunov's auxiliary theorem | Linearizable error dynamics | Nonlinear observers | Nonlinear systems | Siegel domain | Output injection | linearizable error dynamics | nonlinear systems | LINEARIZATION | MATHEMATICS, APPLIED | output injection | nonlinear observers | AUTOMATION & CONTROL SYSTEMS

Siegel's theorem | Lyapunov's auxiliary theorem | Linearizable error dynamics | Nonlinear observers | Nonlinear systems | Siegel domain | Output injection | linearizable error dynamics | nonlinear systems | LINEARIZATION | MATHEMATICS, APPLIED | output injection | nonlinear observers | AUTOMATION & CONTROL SYSTEMS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 8/2018, Volume 90, Issue 4, pp. 1 - 42

We give a detailed description of a $$C^*$$ C∗ -algebra generated by Toeplitz operators acting on the weighted Bergman space over three-dimensional Siegel...

Bergman space | Analysis | Mathematics | Toeplitz operator | Primary 47B35 | Secondary 32A36 | Siegel domain | C-algebra | FOCK SPACE | MATHEMATICS | REPRESENTATIONS | C-ASTERISK-ALGEBRAS | QUANTIZATION | Algebra

Bergman space | Analysis | Mathematics | Toeplitz operator | Primary 47B35 | Secondary 32A36 | Siegel domain | C-algebra | FOCK SPACE | MATHEMATICS | REPRESENTATIONS | C-ASTERISK-ALGEBRAS | QUANTIZATION | Algebra

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 2014, Volume 90, Issue 1, pp. 77 - 89

We show that the modulus of the Bergman kernel B(z, zeta) of a general homogeneous Siegel domain of type II is 'almost constant' uniformly with respect to z...

Bergman space | homogeneous Siegel domain of type II | Bergman mapping | Bergman projector | atomic decomposition | interpolation | Bergman kernel | Bergman metric | TUBE DOMAINS | SYMMETRIC CONES | BERGMAN PROJECTIONS | SPACES | BOUNDEDNESS | MATHEMATICS | DECOMPOSITIONS

Bergman space | homogeneous Siegel domain of type II | Bergman mapping | Bergman projector | atomic decomposition | interpolation | Bergman kernel | Bergman metric | TUBE DOMAINS | SYMMETRIC CONES | BERGMAN PROJECTIONS | SPACES | BOUNDEDNESS | MATHEMATICS | DECOMPOSITIONS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 06/2015, Volume 151, pp. 230 - 262

We prove Galois equivariance of ratios of Petersson inner products of holomorphic cuspforms on symplectic, unitary, or Hermitian orthogonal groups. As a...

Siegel Eisenstein series | Theta series | Siegel–Weil Eisenstein series | Cuspforms | Secondary | Siegel-Weil Eisenstein series | Primary | ZETA-FUNCTIONS | EISENSTEIN SERIES | UNITARY GROUPS | SPECIAL VALUES | CUSPIDALITY | SIEGEL-WEIL FORMULA | MODULAR-FORMS | MATHEMATICS | PULLBACKS | INNER PRODUCTS

Siegel Eisenstein series | Theta series | Siegel–Weil Eisenstein series | Cuspforms | Secondary | Siegel-Weil Eisenstein series | Primary | ZETA-FUNCTIONS | EISENSTEIN SERIES | UNITARY GROUPS | SPECIAL VALUES | CUSPIDALITY | SIEGEL-WEIL FORMULA | MODULAR-FORMS | MATHEMATICS | PULLBACKS | INNER PRODUCTS

Journal Article

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, ISSN 1747-6933, 2017, Volume 62, Issue 9, pp. 1192 - 1203

The goal of this note is to explore the relationship between the Folland-Kohn basic estimate and the Z(q)-condition. In particular, on unbounded domains, we...

MATHEMATICS | Heisenberg group | closed range of partial derivative | strictly pseudoconvex | Siegel upper half space | HARMONIC INTEGRALS | CLOSED RANGE | uniform Z(q) | PSEUDO-CONVEX MANIFOLDS | Z(q) | unbounded domain | PARTIAL-DERIVATIVE(B)

MATHEMATICS | Heisenberg group | closed range of partial derivative | strictly pseudoconvex | Siegel upper half space | HARMONIC INTEGRALS | CLOSED RANGE | uniform Z(q) | PSEUDO-CONVEX MANIFOLDS | Z(q) | unbounded domain | PARTIAL-DERIVATIVE(B)

Journal Article

20.
Full Text
Weighted Integral Representations of Pluriharmonic Functions in the Siegel Domain of C-n

RESULTS IN MATHEMATICS, ISSN 1422-6383, 12/2019, Volume 74, Issue 4

The Siegel domain in the space C-n is defined as follows: Omega(n) ={eta = (eta(1), eta(2),..., eta(n)) is an element of C-n : Im eta(1) > (k=2)Sigma(n)...

MATHEMATICS | MATHEMATICS, APPLIED | weighted function spaces | HOLOMORPHIC FUNCTIONS | weighted integral representations | conjugate pluriharmonic functions | holomorphic and pluriharmonic functions | Siegel domain

MATHEMATICS | MATHEMATICS, APPLIED | weighted function spaces | HOLOMORPHIC FUNCTIONS | weighted integral representations | conjugate pluriharmonic functions | holomorphic and pluriharmonic functions | Siegel domain

Journal Article

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