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12/2015
Motivated by the need of processing functional-valued data, or more general, operatorvalued data, we introduce the notion of the operator reproducing kernel Hilbert space (ORKHS... 
Mathematics - Functional Analysis
Journal Article
Journal of functional analysis, ISSN 0022-1236, 12/2017, Volume 273, Issue 12, pp. 3671 - 3718
A number of recent papers have established connections between reproducing kernel Hilbert spaces H of entire functions, de Branges spaces, sampling formulas and a class of symmetric operators with deficiency indices (1,1... 
Vector valued de Branges spaces | Entire operators | Sampling formulas | Symmetric operators with deficiency indices [formula omitted] | Symmetric operators with deficiency indices (p,p) | Physical Sciences | Mathematics | Science & Technology | Bisphenol-A | Analysis
Journal Article
07/2020, Studies in Systems, Decision and Control, ISBN 9783030512637, Volume 304
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions... 
Book Chapter
04/2011
.... Our characterization shows that the spaces associated with the "classical reproducing kernels," as well as certain natural extensions of these spaces, are precisely those that are... 
Mathematics - Functional Analysis
Journal Article
Integral equations and operator theory, ISSN 0378-620X, 04/1996, Volume 24, Issue 4, pp. 470 - 482
We characterize when positive operators can be factored by ''analytic Toeplitz'' type operators. As a corollary, we give an operator theory characterization of... 
Physical Sciences | Mathematics | Science & Technology
Journal Article
Journal of operator theory, ISSN 0379-4024, 4/2011, Volume 65, Issue 2, pp. 235 - 240
In this note, we prove that an operator between reproducing kernel Hilbert spaces is a multiplication operator if and only if it leaves invariant zero sets... 
Interpolation | Algebra | Analytic functions | Restriction mapping | Uniqueness | Hilbert spaces | Scalars | Mathematical functions | Reproducing kernel Hilbert space | Reflexive algebra | Holomorphic interpolation | Multiplication operator | Physical Sciences | Mathematics | Science & Technology
Journal Article
Complex analysis and operator theory, ISSN 1661-8254, 8/2013, Volume 7, Issue 4, pp. 965 - 981
.... Our characterization shows that the spaces associated with the “classical reproducing kernels” $${z \mapsto (1 - \bar{w}z)^{-\eta}}$$ , where $${w \in \mathbb D}$$ and η > 0... 
Secondary 47B33 | Operator Theory | 47B15 | Analysis | Composition operator | Weighted Hardy space | Primary 47B32 | Mathematics, general | Mathematics | Weighted composition operator | Hermitian operator | Physical Sciences | Mathematics, Applied | Science & Technology
Journal Article
01/2014
In this paper, we give some results concerning atomic decompositions for operators on reproducing kernel Hilbert spaces, using frame theory techniques... 
Mathematics - Functional Analysis
Journal Article
Mathematical Reports (Bucharest), ISSN 1582-3067, 2015, Volume 17, Issue 3, pp. 303 - 314
In this paper, we give some results concerning atomic decompositions for operators on reproducing kernel Hilbert spaces, using frame theory techniques... 
Frames | Reproducing kernel | Bergman spaces | Atomic systems | Fock spaces | Physical Sciences | Mathematics | Science & Technology
Journal Article
Central European journal of mathematics, ISSN 1895-1074, 06/2010, Volume 8, Issue 3, pp. 569 - 596
We study unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have... 
Reproducing kernel | Hilbert space | Function spaces | Linear operator | Physical Sciences | Mathematics | Science & Technology
Journal Article
Journal of nonlinear science, ISSN 0938-8974, 02/2020, Volume 30, Issue 1, pp. 283 - 315
.... We propose kernel transfer operators, which extend transfer operator theory to reproducing kernel Hilbert spaces and show that these operators are related to Hilbert space representations... 
Physical Sciences | Technology | Physics, Mathematical | Mechanics | Mathematics | Mathematics, Applied | Physics | Science & Technology | Computer science | Molecular dynamics | Information management | Analysis | Kernels | Data analysis | Operators | Approximation | Mathematical analysis | Numerical methods | Signal processing | Hilbert space | Eigenvectors | Empirical analysis
Journal Article
07/2018
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions... 
Journal Article
Lithuanian mathematical journal, ISSN 0363-1672, 04/1980, Volume 20, Issue 2, pp. 93 - 99
Journal Article
Houston journal of mathematics, ISSN 0362-1588, 2016, Volume 42, Issue 3, pp. 877 - 903
In this work, we study weighted composition operators acting on a reproducing kernel Hilbert space of analytic functions and mapping into a weighted-type Banach space or a Bloch-type space... 
Reproducing kernel Hilbert space | Weighted composition operator | Weighted Bergman space | Bloch space | Bloch-type space | Hardy space | Physical Sciences | Mathematics | Science & Technology
Journal Article
02/2016
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods... 
Statistics - Machine Learning
Journal Article
Osaka journal of mathematics, ISSN 0030-6126, 07/2015, Volume 52, Issue 3, pp. 581 - 599
.... This article studies the hypercyclicity of translation operators in some general reproducing kernel Hilbert spaces of entire functions... 
Physical Sciences | Mathematics | Science & Technology | 46E22 | 442C15 | 46E20
Journal Article
9/2014, ISBN 1493911058
...–Toeplitz operators and Gabor multipliers. We introduce Gabor–Toeplitz operators and Gabor multipliers as Toeplitz operators defined in the context of general reproducing kernel Hilbert spaces... 
Eigenvalues | Metaplectic representation | Asymptotic boundary form | Fock space | Compact Gabor–Toeplitz operators | Eigenvalue plunge region | Compact Gabor-Toeplitz operators
Book Chapter
Journal of multivariate analysis, ISSN 0047-259X, 01/2019, Volume 169, pp. 166 - 178
.... In this paper, we study shrinkage estimation of the covariance operator in reproducing kernel Hilbert spaces... 
Reproducing kernel Hilbert space | Covariance operator | Minimax lower bound | Rate of convergence | Shrinkage estimator | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology
Journal Article
Positivity : an international journal devoted to the theory and applications of positivity in analysis, ISSN 1572-9281, 04/2017, Volume 21, Issue 4, pp. 1615 - 1623
Journal Article
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