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    Wyświetlanie 1-4 z 4
    Tytuł:
    The asymptotic trace norm of random circulants and the graph energy
    Autorzy:
    Koshkin, Sergiy
    Powiązania:
    https://bibliotekanauki.pl/articles/729702.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    random matrix
    graph energy
    matrix energy
    circulant
    Toeplitz matrix
    band matrix
    Dirichlet kernel
    non-uniform Berry-Esseen estimate
    Talagrand concentration inequality
    Opis:
    We compute the expected normalized trace norm (matrix/graph energy) of random symmetric band circulant matrices and graphs in the limit of large sizes, and obtain explicit bounds on the rate of convergence to the limit, and on the probabilities of large deviations. We also show that random symmetric band Toeplitz matrices have the same limit norm assuming that their band widths remain small relative to their sizes. We compare the limit norms across a range of related random matrix and graph ensembles.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2016, 36, 1-2; 67-92
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the uniform convergence and L¹-convergence of double Walsh-Fourier series
    Autorzy:
    Móricz, Ferenc
    Powiązania:
    https://bibliotekanauki.pl/articles/1293178.pdf
    Data publikacji:
    1992
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Walsh-Paley system
    W-continuity
    moduli of continuity and smoothness
    bounded variation in the sense of Hardy and Krause
    generalized bounded variation
    complementary functions in the sense of W. H. Young
    rectangular partial sum
    Dirichlet kernel
    convergence in $L^p$-norm
    uniform convergence Salem's test
    Dini-Lipschitz test
    Dirichlet-Jordan test
    Opis:
    In 1970 C. W. Onneweer formulated a sufficient condition for a periodic W-continuous function to have a Walsh-Fourier series which converges uniformly to the function. In this paper we extend his results from single to double Walsh-Fourier series in a more general setting. We study the convergence of rectangular partial sums in $L^p$-norm for some 1 ≤ p ≤ ∞ over the unit square [0,1) × [0,1). In case p = ∞, by $L^p$ we mean $C_W$, the collection of uniformly W-continuous functions f(x, y), endowed with the supremum norm. As special cases, we obtain the extensions of the Dini-Lipschitz test and the Dirichlet-Jordan test for double Walsh-Fourier series.
    Źródło:
    Studia Mathematica; 1992, 102, 3; 225-237
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a modification of the Poisson integral operator
    Autorzy:
    Partyka, Dariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/747196.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Dirichlet integral
    eigenvalue of a Jordan curve
    eigenvalue of a quasisymmetric automorphism
    extremal quasiconformal mapping
    Fourier coefficient
    harmonic conjugation operator
    harmonic function
    Neumann-Poincare kernel
    Poisson integral
    Opis:
    Given a quasisymmetric automorphism \(\gamma\) of the unit circle \(\mathbb{T}\) we define and study a modification \(P_{\gamma}\) of the classical Poisson integral operator in the case of the unit disk \(\mathbb{D}\). The modification is done by means of the generalized Fourier coefficients of \(\gamma\). For a Lebesgue’s integrable complexvalued function \(f\) on \(\mathbb{T}\), \(P_{\gamma}[f]\) is a complex-valued harmonic function in \(\mathbb{D}\) and it coincides with the classical Poisson integral of \(f\) provided \(\gamma\) is the identity mapping on \(\mathbb{T}\). Our considerations are motivated by the problem of spectral values and eigenvalues of a Jordan curve. As an application we establish a relationship between the operator \(P_{\gamma}\), the maximal dilatation of a regular quasiconformal Teichmuller extension of \(\gamma\) to \(\mathbb{D}\) and the smallest positive eigenvalue of \(\gamma\).
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2011, 65, 2
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – 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 1-4 z 4

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