2016, Graduate studies in mathematics, ISBN 1470430959, Volume 177, xxiii, 275 pages

Book

Advanced Materials, ISSN 0935-9648, 06/2019, Volume 31, Issue 26, pp. e1806687 - n/a

One of the most ambitious technological goals is the development of devices working under the laws of quantum mechanics. Among others, an important challenge...

molecular spintronics | quantum algorithm | Hilbert space | quantum computing | PHYSICS, CONDENSED MATTER | DESIGN | PHYSICS, APPLIED | MAGNETIZATION | MATERIALS SCIENCE, MULTIDISCIPLINARY | COMPLEXES | CHEMISTRY, PHYSICAL | NANOSCIENCE & NANOTECHNOLOGY | CRYSTAL | ELECTRON-SPIN | CHEMISTRY, MULTIDISCIPLINARY | QUBITS | QUANTUM SEARCH | BIS(PHTHALOCYANINATO)NIOBIUM(IV) | DYNAMICS | MAGNETS | Algorithms | Search algorithms | Data processing | Electron spin | Quantum phenomena | Coupling (molecular) | Organic chemistry | Quantum computing | Lanthanides | Quantum mechanics | Information storage | Coordination compounds | Nuclear spin

molecular spintronics | quantum algorithm | Hilbert space | quantum computing | PHYSICS, CONDENSED MATTER | DESIGN | PHYSICS, APPLIED | MAGNETIZATION | MATERIALS SCIENCE, MULTIDISCIPLINARY | COMPLEXES | CHEMISTRY, PHYSICAL | NANOSCIENCE & NANOTECHNOLOGY | CRYSTAL | ELECTRON-SPIN | CHEMISTRY, MULTIDISCIPLINARY | QUBITS | QUANTUM SEARCH | BIS(PHTHALOCYANINATO)NIOBIUM(IV) | DYNAMICS | MAGNETS | Algorithms | Search algorithms | Data processing | Electron spin | Quantum phenomena | Coupling (molecular) | Organic chemistry | Quantum computing | Lanthanides | Quantum mechanics | Information storage | Coordination compounds | Nuclear spin

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2016, Volume 302, pp. 410 - 432

It is observed that the infinite matrix with entries (mnlog(mn))−1 for m,n≥2 appears as the matrix of the integral operator Hf(s):=∫1/2+∞f(w)(ζ(w+s)−1)dw with...

Carleson measure | Commutation | Multiplicative Hankel forms | Operator norm | Hardy spaces of Dirichlet series | Riemann zeta function | Bohr lift | Hilbert matrix | Infinite dimensional torus | Spectrum | Mellin transform

Carleson measure | Commutation | Multiplicative Hankel forms | Operator norm | Hardy spaces of Dirichlet series | Riemann zeta function | Bohr lift | Hilbert matrix | Infinite dimensional torus | Spectrum | Mellin transform

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 03/2011, Volume 59, Issue 3, pp. 964 - 978

Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool...

Context | Communities | Signal processing algorithms | Machine learning | Calculus | Hilbert space | kernel adaptive filtering | Complex valued nonlinear adaptive filters | Wirtinger's calculus | Kernel | reproducing kernel Hilbert spaces | ALGORITHM | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Kernel functions | Analysis | Gaussian processes | Least squares | Innovations | Signal processing | Studies | Kernels | Algorithms | Mathematical analysis | Tools | Nonlinearity | Mathematical models | Computer Science - Learning

Context | Communities | Signal processing algorithms | Machine learning | Calculus | Hilbert space | kernel adaptive filtering | Complex valued nonlinear adaptive filters | Wirtinger's calculus | Kernel | reproducing kernel Hilbert spaces | ALGORITHM | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Kernel functions | Analysis | Gaussian processes | Least squares | Innovations | Signal processing | Studies | Kernels | Algorithms | Mathematical analysis | Tools | Nonlinearity | Mathematical models | Computer Science - Learning

Journal Article

The European Physical Journal B, ISSN 1434-6028, 9/2017, Volume 90, Issue 9, pp. 1 - 10

Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the...

Condensed Matter Physics | Solid State Physics | Physics, general | Fluid- and Aerodynamics | Complex Systems | Physics | PHYSICS, CONDENSED MATTER | QUANTUM WALK | Atoms | Physics - Quantum Physics

Condensed Matter Physics | Solid State Physics | Physics, general | Fluid- and Aerodynamics | Complex Systems | Physics | PHYSICS, CONDENSED MATTER | QUANTUM WALK | Atoms | Physics - Quantum Physics

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 05/2013, Volume 25, Issue 4, p. 1350006

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical...

Slice regular functions | Operator algebras | Spectral theory | Non-commutative functional calculus | Quaternionic quantum mechanics | Continuous functional calculus C | algebras | Quaternionic Hilbert space | slice regular functions | spectral theory | C-algebras | QUANTIQUE | REGULAR FUNCTIONS | PHYSICS, MATHEMATICAL | non-commutative functional calculus | continuous functional calculus | ALGEBRAS | operator algebras | QUANTUM-MECHANICS | quaternionic quantum mechanics

Slice regular functions | Operator algebras | Spectral theory | Non-commutative functional calculus | Quaternionic quantum mechanics | Continuous functional calculus C | algebras | Quaternionic Hilbert space | slice regular functions | spectral theory | C-algebras | QUANTIQUE | REGULAR FUNCTIONS | PHYSICS, MATHEMATICAL | non-commutative functional calculus | continuous functional calculus | ALGEBRAS | operator algebras | QUANTUM-MECHANICS | quaternionic quantum mechanics

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 10/2017, Volume 222, Issue 2, pp. 787 - 814

We investigate complex structures on twisted Hilbert spaces, with special attention paid to the Kalton–Peck Z 2 space and to the hyperplane problem. For any...

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | INTERPOLATION | MATHEMATICS | THEOREM | BANACH-SPACES | L-P | SUMS | Hilbert space | Research | Mathematical research | Complex systems

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | INTERPOLATION | MATHEMATICS | THEOREM | BANACH-SPACES | L-P | SUMS | Hilbert space | Research | Mathematical research | Complex systems

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 4/2017, Volume 351, Issue 1, pp. 1 - 44

We study determinantal point processes on $${\mathbb{C}}$$ C induced by the reproducing kernels of generalized Fock spaces as well as those on the unit disc...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MATHEMATICAL | GAMMA KERNEL | Derivatives (Financial instruments) | Information management | Dynamical Systems | Mathematics

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MATHEMATICAL | GAMMA KERNEL | Derivatives (Financial instruments) | Information management | Dynamical Systems | Mathematics

Journal Article

9.
Full Text
The minimal model program for the Hilbert scheme of points on P-2 and Bridgeland stability

ADVANCES IN MATHEMATICS, ISSN 0001-8708, 03/2013, Volume 235, pp. 580 - 626

In this paper, we study the birational geometry of the Hilbert scheme P-2[n] of n-points on P-2. We discuss the stable base locus decomposition of the...

MATHEMATICS | ALGEBRAIC FAMILIES | BUNDLES | Hilbert scheme | K3 SURFACES | COMPLEXES | MODULI SPACE | Minimal model program | CURVES | Bridgeland stability conditions | Quiver representations | SEMISTABLE OBJECTS

MATHEMATICS | ALGEBRAIC FAMILIES | BUNDLES | Hilbert scheme | K3 SURFACES | COMPLEXES | MODULI SPACE | Minimal model program | CURVES | Bridgeland stability conditions | Quiver representations | SEMISTABLE OBJECTS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2019, Volume 276, Issue 5, pp. 1622 - 1679

Suppose H is a finite dimensional reproducing kernel Hilbert space of functions on X. If H has the complete Pick property then there is an isometric map, Φ,...

Complete Pick property | Complex hyperbolic space | INTERPOLATION | MATHEMATICS | SHAPE INVARIANT | TRIANGLES | OPERATOR-ALGEBRAS

Complete Pick property | Complex hyperbolic space | INTERPOLATION | MATHEMATICS | SHAPE INVARIANT | TRIANGLES | OPERATOR-ALGEBRAS

Journal Article

11.
Full Text
The Łojasiewicz gradient inequality in the infinite-dimensional Hilbert space framework

Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 260, Issue 9, pp. 2826 - 2842

We provide a reasonably optimal answer to the natural question of the conditions under which an analytic function on an infinite-dimensional Hilbert space...

Gradient inequality | Analytic functionals | Hilbert space | Łojasiewicz theorem | DISSIPATION | DECAY | SEMILINEAR EVOLUTION-EQUATIONS | MATHEMATICS | ANALYTIC NONLINEARITY | EQUILIBRIUM | Lojasiewicz theorem | CONVERGENCE | SYSTEMS | BOUNDED SOLUTIONS | WAVE-EQUATION

Gradient inequality | Analytic functionals | Hilbert space | Łojasiewicz theorem | DISSIPATION | DECAY | SEMILINEAR EVOLUTION-EQUATIONS | MATHEMATICS | ANALYTIC NONLINEARITY | EQUILIBRIUM | Lojasiewicz theorem | CONVERGENCE | SYSTEMS | BOUNDED SOLUTIONS | WAVE-EQUATION

Journal Article

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, ISSN 0219-8878, 05/2019, Volume 16, Issue 5

An orthogonality space is a set endowed with a symmetric, irreflexive binary relation. By means of the usual orthogonality relation, each anisotropic quadratic...

orthogonality space | orthomodular lattice | THEOREM | orthomodular space over an ordered star-field | QUANTUM | Characterization of the complex Hilbert space | PHYSICS, MATHEMATICAL

orthogonality space | orthomodular lattice | THEOREM | orthomodular space over an ordered star-field | QUANTUM | Characterization of the complex Hilbert space | PHYSICS, MATHEMATICAL

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2015, Volume 17, Issue 4, pp. 1550016 - 1-1550016-42

We consider bordered Riemann surfaces which are biholomorphic to compact Riemann surfaces of genus g with n regions biholomorphic to the disk removed. We...

Rigged moduli space | Weil-Petersson class Teichmüller space | MATHEMATICS | MATHEMATICS, APPLIED | Weil-Petersson class Teichmuller space | COMPLEX STRUCTURE | CURVE | Manifolds | Riemann surfaces | Mathematical analysis | Disks | Field theory | Mapping | Inclusions | Expansion | Mathematics | Naturvetenskap | Natural Sciences | Matematik

Rigged moduli space | Weil-Petersson class Teichmüller space | MATHEMATICS | MATHEMATICS, APPLIED | Weil-Petersson class Teichmuller space | COMPLEX STRUCTURE | CURVE | Manifolds | Riemann surfaces | Mathematical analysis | Disks | Field theory | Mapping | Inclusions | Expansion | Mathematics | Naturvetenskap | Natural Sciences | Matematik

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2015, Volume 64, Issue 2, pp. 577 - 612

We introduce and study a class of operator tuples in complex Hilbert spaces, which we call spherical tuples. In particular, we characterize spherical...

Essential p-normality | Taylor spectrum | Joint q-isometry | Jointly hyponormal | Spherical tuple | CIRCULAR OPERATORS | joint q-isometry | C-ASTERISK-ALGEBRAS | SINGULAR INTEGRAL-OPERATORS | jointly hyponormal | MULTIPLICATION OPERATORS | COMMUTATORS | SPECTRAL PROPERTIES | UNIT BALL | WEIGHTED SHIFT | MATHEMATICS | essential p-normality | CLASS HANKEL-OPERATORS | BERGMAN SPACES

Essential p-normality | Taylor spectrum | Joint q-isometry | Jointly hyponormal | Spherical tuple | CIRCULAR OPERATORS | joint q-isometry | C-ASTERISK-ALGEBRAS | SINGULAR INTEGRAL-OPERATORS | jointly hyponormal | MULTIPLICATION OPERATORS | COMMUTATORS | SPECTRAL PROPERTIES | UNIT BALL | WEIGHTED SHIFT | MATHEMATICS | essential p-normality | CLASS HANKEL-OPERATORS | BERGMAN SPACES

Journal Article

Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2014, Volume 39, Issue 1, pp. 231 - 258

If g is an analytic function in the unit disc D, we consider the generalized Hilbert operator H-g defined by H(g()f)(z) = integral(1)(0) f(t)g'(tz)dt. We study...

Dirichlet spaces | Generalized Hilbert operators | Bergman spaces | Hardy spaces | MATHEMATICS | MATRIX | HARDY | ANALYTIC-FUNCTIONS

Dirichlet spaces | Generalized Hilbert operators | Bergman spaces | Hardy spaces | MATHEMATICS | MATRIX | HARDY | ANALYTIC-FUNCTIONS

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 12/2015, Volume 200, pp. 221 - 226

Several interesting formulas concerning finite Hilbert transform and logarithmic integrals are proved with application determining equilibrium measures.

Equilibrium measures | Hilbert transform | Boundary functions | Complex Hardy spaces | MATHEMATICS

Equilibrium measures | Hilbert transform | Boundary functions | Complex Hardy spaces | MATHEMATICS

Journal Article

2007, Graduate texts in mathematics, ISBN 0387354182, Volume 237, xii, 220

Book

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 7240 - 7254

Aveiro method is a sparse representation method in reproducing kernel Hilbert spaces, which gives orthogonal projections in linear combinations of reproducing...

pre‐orthogonal greedy algorithm | Aveiro method | reproducing Kernel | Reproducing Kernel | Pre-orthogonal greedy algorithm | DECOMPOSITION | MATHEMATICS, APPLIED | pre-orthogonal greedy algorithm | Kernels | Greedy algorithms | Dictionaries | Hilbert space | Quantum theory | Uniqueness | Mathematics - Complex Variables

pre‐orthogonal greedy algorithm | Aveiro method | reproducing Kernel | Reproducing Kernel | Pre-orthogonal greedy algorithm | DECOMPOSITION | MATHEMATICS, APPLIED | pre-orthogonal greedy algorithm | Kernels | Greedy algorithms | Dictionaries | Hilbert space | Quantum theory | Uniqueness | Mathematics - Complex Variables

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2015, Volume 276, Issue 2, pp. 287 - 307

We show that Rochberg's generalized interpolation spaces X-(n) arising from analytic families of Banach spaces form exact sequences 0 -> X-(n) -> X(n+k) ->...

Twisted sums of banach spaces | Complex interpolation | MATHEMATICS | BANACH-SPACES | twisted sums of Banach spaces | SUMS | Mathematics - Functional Analysis

Twisted sums of banach spaces | Complex interpolation | MATHEMATICS | BANACH-SPACES | twisted sums of Banach spaces | SUMS | Mathematics - Functional Analysis

Journal Article

ANNALES HENRI POINCARE, ISSN 1424-0637, 11/2018, Volume 19, Issue 11, pp. 3321 - 3355

Quantum Theories can be formulated in real, complex or quaternionic Hilbert spaces as established in Soler's theorem. Quantum states are here pictured in terms...

PHYSICS, MULTIDISCIPLINARY | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS | Atoms | Projectors | Physicists | Quantum theory

PHYSICS, MULTIDISCIPLINARY | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS | Atoms | Projectors | Physicists | Quantum theory

Journal Article

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