共查询到20条相似文献,搜索用时 0 毫秒
1.
Ferenc Móricz 《Analysis Mathematica》2007,33(1):45-54
We give sufficient conditions for the convergence of the double Fourier integral of a complex-valued function f ∈ L 1(?2) with bounded support at a given point (x 0,y 0) ∈ ?2. It turns out that this convergence essentially depends on the convergence of the single Fourier integrals of the marginal functions f(x,y 0), x ∈ ?, and f(x 0,y), y ∈ ?, at the points x:= x 0 and y:= y 0, respectively. Our theorem applies to functions in the multiplicative Zygmund classes of functions in two variables. 相似文献
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Mathematical Notes - We introduce the notion of spherical jump of a function of several variables at a given point with respect to a homogeneous harmonic polynomial. Here, if the function is... 相似文献
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In this short note we consider suitable linear combinations of Bochner-Riesz type multivariate sampling series, which greatly improve the order of pointwise approximation. In particular we state some asymptotic formulae of Voronovskaja type which are of interest in image reconstruction. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Sevgi Esen Almali 《Mathematical Methods in the Applied Sciences》2019,42(16):5346-5353
In this paper, we consider a family of nonlinear integral operators of Urysohn‐type and study the pointwise convergence of the family at characteristic points of L1?function. The kernel Kλ(x,t,u(t)) depends on the positive parameter λ changing on the set of numbers with the accumulation point at infinity and Kλ(x,t,u(t)) is an entire analytic function of variable u, which is a bounded function belonging to L1(R). 相似文献
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《Journal of the Egyptian Mathematical Society》2014,22(3):337-340
In the paper, the authors establish some new inequalities of Qi type for double integrals on a rectangle, from which some known integral inequalities of Qi type may be derived. 相似文献
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We offer an approach by means of Clifford algebra to convergence of Fourier series on unit spheres of even-dimensional Euclidean
spaces. It is based on generalizations of Fueter’s Theorem inducing quaternionic regular functions from holomorphic functions
in the complex plane. We, especially, do not rely on the heavy use of special functions. Analogous Riemann-Lebesgue theorem,
localization principle and a Dini’s type pointwise convergence theorem are proved.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
10.
Let(Ω,Σ,μ)be a complete probability space and let X be a Banach space.We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem.We also obtain a Vitali type I-convergence theorem for Pettis integrals where I is an ideal on N. 相似文献
11.
G. Ts. Tumarkin 《Mathematical Notes》1969,5(4):265-269
In a domain G bounded by a rectifiable Jordan curve γ let there be given a sequence of analytic functions {fn(z)} representable by Cauchy-Lebesgue type integrals $$f_n (z) = \smallint _y \frac{{\omega _n (\zeta )}}{{\zeta - z}}d\zeta .$$ A theorem is established which enables one to determine from the convergence in measure of {ωn(ζ)} on a set e ?γ whether or not there is convergence in measure on the same set of {fn(ζ)}, the angular boundary values of the functionsfn(z). 相似文献
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The note contains two examples of function spaces
C
p
(X) endowed with the pointwise topology. The
first example is C
p
(M), M
being a planar continuum, such that C
p
(M)
m
is
uniformly homeomorphic to C
p
(M)
n
if and only if
m = n. This strengthens earlier results concerning
linear homeomorphisms. The second example is a non-Lindelöf function
space C
p
(X), where X is a
monolithic perfectly normal compact space all linearly orderable closed
subspaces of which are metrizable. This example is obtained under the
additional set-theoretical axiom . This solves a problem of Arhangelskiĭ. 相似文献
14.
Dmitri Shakhmatov 《Topology and its Applications》2010,157(8):1518-324
Let G be a topological group with the identity element e. Given a space X, we denote by Cp(X,G) the group of all continuous functions from X to G endowed with the topology of pointwise convergence, and we say that X is: (a) G-regular if, for each closed set F⊆X and every point x∈X?F, there exist f∈Cp(X,G) and g∈G?{e} such that f(x)=g and f(F)⊆{e}; (b) G?-regular provided that there exists g∈G?{e} such that, for each closed set F⊆X and every point x∈X?F, one can find f∈Cp(X,G) with f(x)=g and f(F)⊆{e}. Spaces X and Y are G-equivalent provided that the topological groups Cp(X,G) and Cp(Y,G) are topologically isomorphic.We investigate which topological properties are preserved by G-equivalence, with a special emphasis being placed on characterizing topological properties of X in terms of those of Cp(X,G). Since R-equivalence coincides with l-equivalence, this line of research “includes” major topics of the classical Cp-theory of Arhangel'ski? as a particular case (when G=R).We introduce a new class of TAP groups that contains all groups having no small subgroups (NSS groups). We prove that: (i) for a given NSS group G, a G-regular space X is pseudocompact if and only if Cp(X,G) is TAP, and (ii) for a metrizable NSS group G, a G?-regular space X is compact if and only if Cp(X,G) is a TAP group of countable tightness. In particular, a Tychonoff space X is pseudocompact (compact) if and only if Cp(X,R) is a TAP group (of countable tightness). Demonstrating the limits of the result in (i), we give an example of a precompact TAP group G and a G-regular countably compact space X such that Cp(X,G) is not TAP.We show that Tychonoff spaces X and Y are T-equivalent if and only if their free precompact Abelian groups are topologically isomorphic, where T stays for the quotient group R/Z. As a corollary, we obtain that T-equivalence implies G-equivalence for every Abelian precompact group G. We establish that T-equivalence preserves the following topological properties: compactness, pseudocompactness, σ-compactness, the property of being a Lindelöf Σ-space, the property of being a compact metrizable space, the (finite) number of connected components, connectedness, total disconnectedness. An example of R-equivalent (that is, l-equivalent) spaces that are not T-equivalent is constructed. 相似文献
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For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of
the Durrmeyer-type operatorsL
f at those points xεIntI at which the one-sided limits f(x±0) exist. In the main theorems the Chanturiya's modulus of variation
is used. 相似文献
17.
R. Chen 《Probability Theory and Related Fields》1976,36(1):75-83
In this paper, first, we prove some inequalities for randomly stopped variables, which arise naturally in the gambling theory, then we show that a theorem of Chacon and some pointwise convergence theorems, which imply the submartingale convergence theorem, are immediate consequences of these inequalities. 相似文献
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V. V. Lebedev 《Mathematical Notes》2012,91(5-6):889-892
19.
Let f: R
N
→ C be a periodic function with period 2π in each variable. We prove suffcient conditions for the absolute convergence of the multiple Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial
derivative in case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to multiple
Fourier series.
This research was started while the first author was a visiting professor at the Department of Mathematics, Texas A&M University,
College Station during the fall semester in 2005; and it was also supported by the Hungarian National Foundation for Scientific
Research under Grant T 046 192. 相似文献
20.
W Stadler 《Journal of Mathematical Analysis and Applications》1973,42(2):409-412
A Dirichlet-type7 theorem for the uniform convergence of integrals of the form ∝∞0cos(tf(α)) cos(xα) dα is given. The theorem is illustrated by an application in the solution of a simple fourth order partial differential equation. 相似文献