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    Wyświetlanie 1-8 z 8
    Tytuł:
    On some subclasses of the family of Darboux Baire 1 functions
    Autorzy:
    Ivanova, G.
    Wagner-Bojakowska, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255127.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Darboux property
    Baire property
    I-approximate continuity
    quasi-continuity
    strong Świątkowski property
    Opis:
    We introduce a subclass of the family of Darboux Baire 1 functions f : R → R modifying the Darboux property analogously as it was done by Z. Grande in [On a subclass of the family of Darboux functions, Colloq. Math. 17 (2009), 95–104], and replacing approximate continuity with I-approximate continuity, i.e. continuity with respect to the I-density topology. We prove that the family of all Darboux quasi-continuous functions from the first Baire class is a strongly porous set in the space DB1 of Darboux Baire 1 functions, equipped with the supremum metric.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 777-788
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convolution algebras for topological groupoids with locally compact fibres
    Autorzy:
    Buneci, M. R.
    Powiązania:
    https://bibliotekanauki.pl/articles/254971.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    convolution algebra
    groupoid
    uniform continuity
    Haar system
    Opis:
    The aim of this paper is to introduce various convolution algebras associated with a topological groupoid with locally compact fibres. Instead of working with continuous functions on G, we consider functions having a uniformly continuity property on fibres. We assume that the groupoid is endowed with a system of measures (supported on its fibres) subject to the "left invariance" condition in the groupoid sense.
    Źródło:
    Opuscula Mathematica; 2011, 31, 2; 159-172
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On one condition of absolutely continuous spectrum for self-adjoint operators and its applications
    Autorzy:
    Ianovich, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/254841.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    self-adjoint operators absolutely continuous spectrum
    equi-absolute continuity
    spectral density
    Jacobi matrices
    Opis:
    In this work the method of analyzing of the absolutely continuous spectrum for self-adjoint operators is considered. For the analysis it is used an approximation of a self-adjoint operator A by a sequence of operators An with absolutely continuous spectrum on a given interval [a, b] which converges to A in a strong sense on a dense set. The notion of equi-absolute continuity is also used. It was found a sufficient condition of absolute continuity of the operator A spectrum on the finite interval [a, b] and the condition for that the corresponding spectral density belongs to the class Lp[a,b] (p ≥ 1). The application of this method to Jacobi matrices is considered. As one of the results we obtain the following assertion: Under some mild assumptions, suppose that there exist a constant C > 0 and a positive function g(x) ∈ Lp[a, b] (p ≥ 1).such that for all n sufficiently large and almost all [formula] the estimate [formula] holds, where Pn(x) are 1st type polynomials associated with Jacobi matrix (in the sense of Akhiezer) and bn is a second diagonal sequence of Jacobi matrix. Then the spectrum of Jacobi matrix operator is purely absolutely continuous on [a, b] and for the corresponding spectral density ƒ (x) we have ƒ (x) ∈ Lp[a,b].
    Źródło:
    Opuscula Mathematica; 2018, 38, 5; 699-718
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Subadditive periodic functions
    Autorzy:
    Matkowski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255656.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    subadditive function
    periodic function
    periodic extension
    concave function
    continuity
    continuous nowhere differentiable function
    Opis:
    Some conditions under which any subadditive function is periodic are presented. It is shown that the boundedness from below in a neighborhood of a point of a subadditive periodic (s.p.) function implies its nonnegativity, and the boundedness from above in a neighborhood of a point implies it nonnegativity and global boundedness from above. A necessary and sufficient condition for existence of a subadditive periodic extension of a function ƒ0 : [0, 1) ? R is given. The continuity, differentiability of a s.p. function is discussed, and an example of a continuous nowhere differentiable s.p. function is presented. The functions which are the sums of linear functions and s.p. functions are characterized. The refinements of some known results on the continuity of subadditive functions are presented.
    Źródło:
    Opuscula Mathematica; 2011, 31, 1; 75-96
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The basis property of eigenfunctions in the problem of a nonhomogeneous damped string
    Autorzy:
    Rzepnicki, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/254937.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonhomogeneous damped string
    Hilbert space
    Riesz basis
    modulus of continuity
    basis with parentheses
    string equation
    Opis:
    The equation which describes the small vibrations of a nonhomogeneous damped string can be rewritten as an abstract Cauchy problem for the densely defined closed operator iA. We prove that the set of root vectors of the operator A forms a basis of subspaces in a certain Hilbert space H. Furthermore, we give the rate of convergence for the decomposition with respect to this basis. In the second main result we show that with additional assumptions the set of root vectors of the operator A is a Riesz basis for H.
    Źródło:
    Opuscula Mathematica; 2017, 37, 1; 141-165
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some properties of set-valued sine families
    Autorzy:
    Mainka-Niemczyk, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255987.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    set-valued sine and cosine families
    continuity of sine families
    Hukuhara differences
    concave set-valued functions
    Opis:
    Let {Ft : t ≥ 0} be a family of continuous additive set-valued functions defined on a convex cone K in a normed linear space X with nonempty convex compact values in X. It is shown that (under some assumptions) a regular sine family associated with {Ft : t ≥ 0} is continuous {Ft : t ≥ 0} is a continuous cosine family.
    Źródło:
    Opuscula Mathematica; 2012, 32, 1; 159-170
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions
    Autorzy:
    Wang, J.
    Yan, X.
    Zhang, X. H.
    Wang, T. M
    Li, X. Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/255673.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    integrodifferential equations
    fractional derivative
    nonlocal conditions
    resolvent operator and their norm continuity
    fixed point theorem
    mild solutions
    Opis:
    In this paper, we discuss a class of integrodifferential equations with nonlocal conditions via a fractional derivative of the type: [formula]. Some sufficient conditions for the existence of mild solutions for the above system are given. The main tools are the resolvent operators and fixed point theorems due to Banach's fixed point theorem, Krasnoselskii's fixed point theorem and Schaefer's fixed point theorem. At last, an example is given for demonstration.
    Źródło:
    Opuscula Mathematica; 2011, 31, 1; 119-135
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On ∞-entropy points in real analysis
    Autorzy:
    Korczak-Kubiak, E.
    Loranty, A.
    Pawlak, R. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255548.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    topological entropy
    Darboux function
    almost continuity
    Baire one function
    approximately continuous function
    pseudo fixed point
    topology of uniform convergence
    compact-open topology
    infinity-entropy point
    Opis:
    We will consider ∞-entropy points in the context of the possibilities of approximation mappings by the functions having ∞-entropy points and belonging to essential (from the point of view of real analysis theory) classes of functions: almost continuous, Darboux Baire one and approximately continuous functions.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 799-812
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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