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    Wyświetlanie 1-9 z 9
    Tytuł:
    A note on inductive limit model of Bargmann space of infinite order
    Autorzy:
    Stochel, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255113.pdf
    Data publikacji:
    2005
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Hilbert space
    Bargmann space
    creation operator
    annihilation operator
    inductive limit
    Opis:
    It is shown that the generalized creation and annihilation operators on Bargmann space of infinite order in a direction a = (a1, a2, ...) mem l2 are inductive limits of the creation and annihilation operator acting on Bargmann space on n-th order.
    Źródło:
    Opuscula Mathematica; 2005, 25, 1; 139-148
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of Greens operator to quadratic variational problems
    Autorzy:
    Azbelev, N. V.
    Tsalyuk, V. Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/255629.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    quadratic variational problem
    Sobolev space
    boundary value problem
    Hilbert space
    Green's operator
    Fredholm integral operator
    spectrum
    Opis:
    We use Green's function of a suitable boundary value problem to convert the variational problem with quadratic functional and linear constraints to the equivalent unconstrained extremal problem in some subspace of the space L2 of quadratically summable functions. We get the neccessary and sufficient criterion for unique solvability of the variational problem in terms of the spectrum of some integral Hilbert-Schmidt operator in L2 with symmetric kernel. The numerical technique is proposed to estimate this criterion. The results are demonstrated on examples: 1) a variational problem with deviating argument, and 2) the problem of the critical force for the vertical pillar with additional support point (the qualities of the pillar may vary discontinuously along the pillar's axis).
    Źródło:
    Opuscula Mathematica; 2006, 26, 2; 243-256
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Operator fractional-linear transformations: convexity and compactness of image; applications
    Autorzy:
    Khatskevich, V.
    Shul'Man, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/1388601.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Hilbert space
    fractional-linear transformation
    evolution operator
    indefinite metric
    Opis:
    The present paper consists of two parts. In Section 1 we consider fractional-linear transformations (f.-l.t. for brevity) F in the space $ℒ(X_1,X_2)$ of all linear bounded operators acting from $X_1$ into $X_2$, where $X_1, X_2$ are Banach spaces. We show that in the case of Hilbert spaces $X_1, X_2$ the image F(ℬ) of any (open or closed) ball ℬ ⊂ D(F) is convex, and if ℬ is closed, then F(ℬ) is compact in the weak operator topology (w.o.t.) (Theorem 1.2). These results extend the corresponding results on compactness obtained in [3], [4] under some additional restrictions imposed on F. We also establish that the convexity of the image of f.-l.t. is a characteristic property of Hilbert spaces, that is, if for the f.-l.t. $F:K → (I+K)^{-1}$ the image $F()$ of the open unit ball of the space ℒ(X) is convex, then X is a Hilbert space (Theorem 1.3). In Section 2 we apply the compactness of F(̅) for the closed unit operator ball ̅ to the study of the behavior of solutions to evolution problems in a Hilbert space ℋ. Namely, we establish the exponential dichotomy of solutions for the so-called hyperbolic case (such that the evolution operator is invertible). This is an extension of Theorem 1.1 of [5], where the corresponding assertion was established for the particular case of a Pontryagin space ℋ.
    Źródło:
    Studia Mathematica; 1995, 116, 2; 189-195
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A remark on generalized commutation relation and subnormality
    Autorzy:
    Stochel, J.B.
    Powiązania:
    https://bibliotekanauki.pl/articles/254981.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Hilbert space
    generalized commutation relations
    creation operator
    analytic vectors
    Opis:
    Tillmann [11] proved that every operator A which fulfils the canonical commutation relation A*A - AA* = Id is an orthogonal sum of canonical creation operators. We extend this result for operators which fulfil generalized commutation relation A*A - AA* = E², where EA = AE. In addition, some inequalities which are helpful in describing analytic vectors of operators A*A, where A fulfils the generalized commutation relation, are established.
    Źródło:
    Opuscula Mathematica; 2006, 26, 1; 151-160
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Singular integral models for p-hyponormal operators and the Riemann-Hilbert problem
    Autorzy:
    Chō, Muneo
    Huruya, Tadasi
    Itoh, Masuo
    Powiązania:
    https://bibliotekanauki.pl/articles/1218219.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Hilbert space
    p-hyponormal operator
    singular integral model
    Riemann-Hilbert problem
    Opis:
    The purpose of this paper is to give singular integral models for p-hyponormal operators and apply them to the Riemann-Hilbert problem.
    Źródło:
    Studia Mathematica; 1998, 130, 3; 213-221
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A sampling theory for infinite weighted graphs
    Autorzy:
    Jorgensen, P. E. T.
    Powiązania:
    https://bibliotekanauki.pl/articles/254989.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    weighted graph
    Hilbert space
    Laplace operator
    sampling
    Shannon
    white noise
    Wiener transform
    interpolation
    Opis:
    We prove two sampling theorems for infinite (countable discrete) weighted graphs G; one example being "large grids of resistors" i.e., networks and systems of resistors. We show that there is natural ambient continuum X containing G, and there are Hilbert spaces of functions on X that allow interpolation by sampling values of the functions restricted only on the vertices in G. We sample functions on X from their discrete values picked in the vertex-subset G. We prove two theorems that allow for such realistic ambient spaces X for a fixed graph G, and for interpolation kernels in function Hilbert spaces on X, sampling only from points in the subset of vertices in G. A continuum is often not apparent at the outset from the given graph G. We will solve this problem with the use of ideas from stochastic integration.
    Źródło:
    Opuscula Mathematica; 2011, 31, 2; 209-236
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Gradient method for non-injective operators in Hilbert space with application to Neumann problems
    Autorzy:
    Karátson, János
    Powiązania:
    https://bibliotekanauki.pl/articles/1338793.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Neumann boundary value problems
    non-injective non-linear operator
    gradient method
    Hilbert space
    Opis:
    The gradient method is developed for non-injective non-linear operators in Hilbert space that satisfy a translation invariance condition. The focus is on a class of non-differentiable operators. Linear convergence in norm is obtained. The method can be applied to quasilinear elliptic boundary value problems with Neumann boundary conditions.
    Źródło:
    Applicationes Mathematicae; 1999, 26, 3; 333-346
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Topological dual of $B_∞(I, ₁(X,Y))$ with application to stochastic systems on Hilbert space
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729390.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    representation theory
    topological dual
    finitely additive operator-valued measures
    polish space
    Hilbert space
    stochastic systems
    structural control
    uncertainty abatement
    Opis:
    In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural control, is to be chosen so as to minimize fluctuation (volatility). Both existence of optimal policy and necessary conditions of optimality are presented including a conceptual algorithm.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 67-90
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some extensions of the a-model
    Autorzy:
    Jursenas, Rytis
    Powiązania:
    https://bibliotekanauki.pl/articles/255405.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    finite rank higher order singular perturbation
    cascade (A) model
    peak model
    Hilbert space
    scale of Hilbert spaces
    Pontryagin space
    ordinary boundary triple
    Krein Q-function
    Weyl function
    gamma field
    symmetric operator
    proper extension
    resolvent
    Opis:
    The A-model for finite rank singular perturbations of class [formula], is considered from the perspective of boundary relations. Assuming further that the Hilbert spaces [formula] admit an orthogonal decomposition [formula], with the corresponding projections satisfying [formula], nontrivial extensions in the A-model are constructed for the symmetric restrictions in the subspaces.
    Źródło:
    Opuscula Mathematica; 2020, 40, 5; 569-597
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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