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    Wyświetlanie 1-10 z 10
    Tytuł:
    Complementation in spaces of symmetric tensor products and polynomials
    Autorzy:
    Blasco, Fernando
    Powiązania:
    https://bibliotekanauki.pl/articles/1220111.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    symmetric tensor
    polynomial
    complementation
    Opis:
    For a locally convex space E we prove that the space of n-symmetric tensors is complemented in the space of (n+1)-symmetric tensors endowed with the projective topology. Applications and related results are also given.
    Źródło:
    Studia Mathematica; 1997, 123, 2; 165-173
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the invertibility of isometric semigroup representations
    Autorzy:
    Batty, C. J. K.
    Greenfield, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/1290204.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    semigroup
    isometric representation
    spectrum
    polynomial convexity
    Opis:
    Let T be a representation of a suitable abelian semigroup S by isometries on a Banach space. We study the spectral conditions which will imply that T(s) is invertible for each s in S. On the way we analyse the relationship between the spectrum of T, Sp(T,S), and its unitary spectrum $Sp_{u}(T,S)$. For $S = ℤ^{n}_{+}$ or $ℝ^{n}_{+}$, we establish connections with polynomial convexity.
    Źródło:
    Studia Mathematica; 1994, 110, 3; 235-250
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pointwise inequalities for Sobolev functions and some applications
    Autorzy:
    Bojarski, Bogdan
    Hajłasz, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/1292626.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Sobolev function
    Taylor polynomial
    approximation
    integral representation
    Bessel capacity
    Opis:
    We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer's theorem which states that Sobolev functions can be approximated by $C^m$ functions both in norm and capacity.
    Źródło:
    Studia Mathematica; 1993, 106, 1; 77-92
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Factorization of weakly continuous holomorphic mappings
    Autorzy:
    González, Manuel
    Gutiérrez, Joaqín
    Powiązania:
    https://bibliotekanauki.pl/articles/1287688.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    weakly continuous holomorphic mapping
    factorization of holomorphic mappings
    polynomial
    weakly continuous multilinear mapping
    Opis:
    We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping ƒ between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form f = g∘S, where S is a compact operator and g a holomorphic mapping.
    Źródło:
    Studia Mathematica; 1996, 118, 2; 117-133
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Polynomial asymptotics and approximation of Sobolev functions
    Autorzy:
    Hajłasz, Piotr
    Kałamajska, Agnieszka
    Powiązania:
    https://bibliotekanauki.pl/articles/1289688.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Sobolev space
    Beppo Levi space
    approximation
    polynomial asymptotics
    density of $C_0^∞$ functions
    Opis:
    We prove several results concerning density of $C_{0}^{∞}$, behaviour at infinity and integral representations for elements of the space $L^{m,p} = {⨍ | ∇^{m}⨍ ∈ L^p}$.
    Źródło:
    Studia Mathematica; 1995, 113, 1; 55-64
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An uncertainty principle related to the Poisson summation formula
    Autorzy:
    Gröchenig, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/1221102.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    uncertainty principle
    Poisson summation formula
    unimodular polynomial
    modulation space
    time-frequency analysis
    phase space
    Opis:
    We prove a class of uncertainty principles of the form $∥S_{g}f∥_{1} ≤ C(∥x^{a}f∥_{p} + ∥ω^{b}f̂∥_{q})$, where $S_{g}f$ is the short time Fourier transform of f. We obtain a characterization of the range of parameters a,b,p,q for which such an uncertainty principle holds. Counter-examples are constructed using Gabor expansions and unimodular polynomials. These uncertainty principles relate the decay of f and f̂ to their behaviour in phase space. Two applications are given: (a) If such an inequality holds, then the Poisson summation formula is valid with absolute convergence of both sums. (b) The validity of an uncertainty principle implies sufficient conditions on a symbol σ such that the corresponding pseudodifferential operator is of trace class.
    Źródło:
    Studia Mathematica; 1996, 121, 1; 87-104
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A weighted Plancherel formula II. The case of the ball
    Autorzy:
    Zhang, Genkai
    Powiązania:
    https://bibliotekanauki.pl/articles/1293186.pdf
    Data publikacji:
    1992
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Plancherel formula
    Harish-Chandra c-function
    reproducing kernel
    orthogonal polynomial
    invariant Cauchy-Riemann operator
    Opis:
    The group SU(1,d) acts naturally on the Hilbert space $L²(B dμ_α) (α > -1)$, where B is the unit ball of $ℂ^d$ and $dμ_α$ the weighted measure $(1-|z|²)^α dm(z)$. It is proved that the irreducible decomposition of the space has finitely many discrete parts and a continuous part. Each discrete part corresponds to a zero of the generalized Harish-Chandra c-function in the lower half plane. The discrete parts are studied via invariant Cauchy-Riemann operators. The representations on the discrete parts are equivalent to actions on some holomorphic tensor fields.
    Źródło:
    Studia Mathematica; 1992, 102, 2; 103-120
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Linear extension operators for restrictions of function spaces to irregular open sets
    Autorzy:
    Rychkov, V. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1206076.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Sobolev spaces
    Besov-Triebel-Lizorkin spaces
    restrictions
    extension operators
    irregular domains
    Hausdorff content
    local polynomial approximation
    complemented subspaces
    Opis:
    Let an open set $Ω ⊂ ℝ^n$ satisfy for some 0≤d≤n and ε > 0 the condition: the $d$-Hausdorff content $H_d(Ω∩B) ≥ ε|B|^{d/n}$ for any ball B centered in Ω of volume |B|≤1. Let $H_p^s$ denote the Bessel potential space on $ℝ^n$ 1 < p < ∞,s > 0, and let $H_p^s[Ω]$ be the linear space of restrictions of elements of $H_p^s$ to Ω endowed with the quotient space norm. We find sufficient conditions for the existence of a linear extension operator for $H_p^s[Ω]$, i.e., a bounded linear operator $H_p^s[Ω]→H_p^s$ such that $ext⨍|_Ω}=⨍$ for all ⨍. The main result is that such an operator exists if (i) d > n-1 and s > (n-d)/min(p,2), or (ii) d≤n-1 and s-[s] > (n-d)/min(p,2). It is an open problem whether these assumptions are sharp.
    Źródło:
    Studia Mathematica; 2000, 140, 2; 141-162
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Polynomial selections and separation by polynomials
    Autorzy:
    Wąsowicz, Szymon
    Powiązania:
    https://bibliotekanauki.pl/articles/1287380.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    separation theorem
    set-valued function
    selection
    n-convex function
    n-concave function
    affine function
    Helly's theorem
    Lagrange interpolating polynomial
    Opis:
    K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
    Źródło:
    Studia Mathematica; 1996, 120, 1; 75-82
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the exponential Orlicz norms of stopped Brownian motion
    Autorzy:
    Peškir, Goran
    Powiązania:
    https://bibliotekanauki.pl/articles/1288072.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Brownian motion (Wiener process)
    stopping time
    exponential Young function
    exponential Orlicz norm
    Doob's maximal inequality for martingales
    Burkholder-Gundy's inequality
    Davis' best constants
    Hermite polynomial
    continuous (local) martingale
    Ito's integral
    the quadratic variation process
    time change (of Brownian motion)
    Kahane-Khinchin's inequalities
    Opis:
    Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by $ψ_p(x) = exp(|x|^p)-1$ with 0 < p ≤ 2) of $max_{0≤t≤τ}|B_t|$ or $|B_τ|$ to be finite, where $B = (B_t)_{t≥0}$ is a standard Brownian motion and τ is a stopping time for B. The conditions are in terms of the moments of the stopping time τ. For instance, we find that $∥max_{0≤t≤τ}|B_t|∥_{ψ_1} < ∞$ as soon as $E(τ^{k}) = O(C^{k}k^{k})$ for some constant C > 0 as k → ∞ (or equivalently $∥τ∥_{ψ_1} < ∞$). In particular, if τ ∼ Exp(λ) or $|N(0,σ^2)|$ then the last condition is satisfied, and we obtain $∥max_{0≤t≤τ}|B_t|∥_{ψ_1} ≤ K √{E(τ)}$ with some universal constant K > 0. Moreover, this inequality remains valid for any class of stopping times τ for B satisfying $E(τ^{k}) ≤ C(Eτ)^{k}k^{k}$ for all k ≥ 1 with some fixed constant C > 0. The method of proof relies upon Taylor expansion, Burkholder-Gundy's inequality, best constants in Doob's maximal inequality, Davis' best constants in the $L^p$-inequalities for stopped Brownian motion, and estimates of the smallest and largest positive zero of Hermite polynomials. The results extend to the case of any continuous local martingale (by applying the time change method of Dubins and Schwarz).
    Źródło:
    Studia Mathematica; 1995-1996, 117, 3; 253-273
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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