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    Wyświetlanie 1-8 z 8
    Tytuł:
    Matrices related to some Fock space operators
    Autorzy:
    Rudol, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/254939.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    frames
    operators
    Fock space
    reproducing kernel
    Opis:
    Matrices of operators with respect to frames are sometimes more natural and easier to compute than the ones related to bases. The present work investigates such operators on the Segal-Bargmann space, known also as the Fock space. We consider in particular some properties of matrices related to Toeplitz and Hankel operators. The underlying frame is provided by normalised reproducing kernel functions at some lattice points.
    Źródło:
    Opuscula Mathematica; 2011, 31, 2; 289-296
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry
    Autorzy:
    Alpay, Daniel
    Jorgensen, Palle E.T.
    Powiązania:
    https://bibliotekanauki.pl/articles/2051893.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    reproducing kernel
    positive definite functions
    approximation
    algorithms
    measures
    stochastic processes
    Opis:
    We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysis and metric geometry and provide a number of examples.
    Źródło:
    Opuscula Mathematica; 2021, 41, 3; 283-300
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Functional models for Nevanlinna families
    Autorzy:
    Behrndt, J.
    Hassi, S.
    Snoo, H. de
    Powiązania:
    https://bibliotekanauki.pl/articles/255065.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    symmetric operator
    selfadjoint extension
    boundary relation
    Weyl family
    functional model
    reproducing kernel Hilbert space
    Opis:
    The class of Nevanlinna families consists of R-symmetric holomorphic multivalued functions on C \ R with maximal dissipative (maximal accumulative) values on C+ (C-, respectively) and is a generalization of the class of operator-valued Nevanlinna functions. In this note Nevanlinna families are realized as Weyl families of boundary relations induced by multiplication operators with the independent variable in reproducing kernel Hilbert spaces.
    Źródło:
    Opuscula Mathematica; 2008, 28, 3; 233-245
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Conditional mean embedding and optimal feature selection via positive definite kernels
    Autorzy:
    Jorgensen, Palle E.T.
    Song, Myung-Sin
    Tiang, James
    Powiązania:
    https://bibliotekanauki.pl/articles/29519641.pdf
    Data publikacji:
    2024
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    positive-definite kernels
    reproducing kernel Hilbert space
    stochastic processes
    frames
    machine learning
    embedding problem
    optimization
    Opis:
    Motivated by applications, we consider new operator-theoretic approaches to conditional mean embedding (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and constructive learning algorithms. For initially given non-linear data, we consider optimization-based feature selections. This entails the use of convex sets of kernels in a construction of optimal feature selection via regression algorithms from learning models. Thus, with initial inputs of training data (for a suitable learning algorithm), each choice of a kernel K in turn yields a variety of Hilbert spaces and realizations of features. A novel aspect of our work is the inclusion of a secondary optimization process over a specified convex set of positive definite kernels, resulting in the determination of “optimal” feature representations.
    Źródło:
    Opuscula Mathematica; 2024, 44, 1; 79-103
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels
    Autorzy:
    Castro, L. P.
    Saitoh, S.
    Tuan, N. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/256011.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Hilbert space
    linear transform
    reproducing kernel
    linear mapping
    convolution
    norm inequality
    integral equation
    Tikhonov regularization
    Opis:
    This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).
    Źródło:
    Opuscula Mathematica; 2012, 32, 4; 633-646
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Finitely additive functions in measure theory and applications
    Autorzy:
    Alpay, Daniel
    Jorgensen, Palle
    Powiązania:
    https://bibliotekanauki.pl/articles/29519748.pdf
    Data publikacji:
    2024
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Hilbert space
    reproducing kernel
    probability space
    Gaussian field
    transforms
    covariance
    Itô integration
    Itô calculus
    generalized Brownian motion
    Opis:
    In this paper, we consider, and make precise, a certain extension of the Radon–Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of μ-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures μ, and to adjoints of composition operators.
    Źródło:
    Opuscula Mathematica; 2024, 44, 3; 323-339
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Decomposition of Gaussian processes, and factorization of positive definite kernels
    Autorzy:
    Jorgensen, Palie E. T.
    Tian, Feng
    Powiązania:
    https://bibliotekanauki.pl/articles/255819.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    reproducing kernel Hilbert space frames
    generalized Ito-integration
    the measurable category analysis/synthesis
    interpolation
    Gaussian free fields
    non-uniform sampling
    optimization
    transform
    covariance
    feature space
    Opis:
    We establish a duality for two lactorization questions, one for general positive definite (p.d.) kernels K, and the other for Gaussian processes, say V. The latter notion, for Gaussian processes is stated via Ito-integration. Our approach to factorization for p.d. kernels is intuitively motivated by matrix factorizations, but in infinite dimensions, subtle measure theoretic issues must be addressed. Consider a given p.d. kernel K, presented as a covariance kernel for a Gaussian process V. We then give an explicit duality for these two seemingly different notions of factorization, for p.d. kernel K, vs for Gaussian process V. Our result is in the form of an explicit correspondence. It states that the analytic data which determine the variety of factorizations for K is the exact same as that which yield factorizations for V. Examples and applications are included: point-processes, sampling schemes, constructive discretization, graph-Laplacians, and boundary-value problems.
    Źródło:
    Opuscula Mathematica; 2019, 39, 4; 497-541
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Frames and factorization of graph Laplacians
    Autorzy:
    Jorgensen, P.
    Tian, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/255936.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    unbounded operators
    deficiency-indices
    Hilbert space
    boundary values
    weighted graph
    reproducing kernel
    Dirichlet form
    graph Laplacian
    resistance network
    harmonic analysis
    frame
    Parseval frame
    Friedrichs extension
    reversible random walk
    resistance distance
    energy Hilbert space
    Opis:
    Using functions from electrical networks (graphs with resistors assigned to edges), we prove existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert space [formula] of a prescribed infinite (or finite) network. Outside degenerate cases, our Parseval frame is not an orthonormal basis. We apply our frame to prove a number of explicit results: With our Parseval frame and related closable operators in [formula] we characterize the Priedrichs extension of the [formula]-graph Laplacian. We consider infinite connected network-graphs G = (V, E), V for vertices, and E for edges. To every conductance function c on the edges E of G, there is an associated pair [formula] where [formula] in an energy Hilbert space, and Δ (=Δc) is the c-graph Laplacian; both depending on the choice of conductance function c. When a conductance function is given, there is a current-induced orientation on the set of edges and an associated natural Parseval frame in [formula] consisting of dipoles. Now Δ is a well-defined semibounded Hermitian operator in both of the Hilbert [formula] and [formula]. It is known to automatically be essentially selfadjoint as an [formula]-operator, but generally not as an [formula] operator. Hence as an [formula] operator it has a Friedrichs extension. In this paper we offer two results for the Priedrichs extension: a characterization and a factorization. The latter is via [formula].
    Źródło:
    Opuscula Mathematica; 2015, 35, 3; 293-332
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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