共查询到20条相似文献,搜索用时 31 毫秒
1.
A. L. Smirnov 《Journal of Mathematical Sciences》2008,151(3):3052-3068
2.
A. V. Glushak 《Mathematical Notes》1995,58(1):703-709
We obtain an integral representation for the solution to the Cauchy problem
相似文献
3.
Nicolae Popescu Marian Vâjâitu Alexandru Zaharescu 《Algebras and Representation Theory》2006,9(1):47-66
Let T be a transcendental element of
and
the orbit of T. On
we have a Haar measure
. The goal of this paper is to characterize all the elements of
for which the integral
, called the trace of T, is well defined.Presented by A. Verschoren 相似文献
4.
We extend the results of Rubio de Francia and Bourgain by showing that, for arbitrary mutually disjoint intervals Δk ⊂ ℤ+, arbitrary p ∈, (0, 2], and arbitrary trigonometric polynomials f
k with supp
, we have
5.
Kai WANG 《数学年刊B辑(英文版)》2007,28(3):321-326
Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd). 相似文献
6.
N. I. Osetinskii 《Computational Mathematics and Modeling》2008,19(1):45-56
We consider the classification of generalized linear controllable systems over the field
= ℂ or
= ℝ under transformations defined by the action of the group GL
n
(
) × GL
n
(
). We review the recent results of Cobb, Helmke, Shayman, Zhou, Hinrichsen, O’Halloran, and others on the geometric structure
of the set of orbits C
n,m
(
) of generalized linear controllable systems, which in particular prove smoothness, compactness, and projectivity of C
n,m
(
) and evaluate its dimension. We show that C
n,m
(
) is a natural compactification of the set of orbits of ordinary linear controllable systems ∑
n,m
(
) and the boundary C
n,m
(
) − ∑
n,m
(
) consists of the orbits of singular generalized systems.
__________
Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 153–166, 2004. 相似文献
7.
A. B. Aleksandrov 《Journal of Mathematical Sciences》2000,101(3):3049-3052
We present an example of a set {
} satisfying the following two conditions: (1) there exists a nonzero positive singular measure on the unit circle {
} with spectrum in Λ; (2) if the spectrum of f∈L1 {
} is contained in Λ and f vanishes on a set of positive measure, then f=0. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 7–14.
Translated by A. B. Aleksandrov. 相似文献
8.
9.
A. G. Babenko 《Mathematical Notes》1996,60(3):248-263
In this paper we prove the Jackson-Stechkin inequalityE
n−1(f)<ω
n
(f, 2τ
n
,λ),n≥1,m≥5,r≥1, f ∈L2(
),f ≢ const, which is sharp for eachn=2, 3, ...; hereE
n−1
(f) is the best approximation of a functionf by spherical polynomials of degree ≤n−1, ω
n
(f, τ) is theτth modulus of continuity off based on the translations
,t ∈ ℝ,x ∈
,
,
is the measure of the unit Euclidean sphere
,
, andτ
n
,λ is the first positive zero of the Gegenbauer cosine polynomial
(cost).
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 333–355, September, 1996.
The present paper was discussed at Ural State University in a seminar headed by Professor Arestov. The author is grateful
to Professor Arestov and Associate Professor Popov for useful conversations.
This research was supported by the State Commission for Higher Education of the Russian Federation under grant No. 2-16-5-31
and by the Russian Foundation for Basic Research under grant No. 93-011-196. 相似文献
10.
L. G. Arabadzhyan 《Mathematical Notes》1997,62(3):271-277
We study the solvability of the integral equation
11.
F. Brackx H. De Schepper N. De Schepper F. Sommen 《Advances in Applied Clifford Algebras》2007,17(3):311-330
Orthogonal Clifford analysis in flat m–dimensional Euclidean space focusses on monogenic functions, i.e. null solutions of the rotation invariant vector valued
Dirac operator
, where (
) forms an orthogonal basis for the quadratic space
underlying the construction of the Clifford algebra
. When allowing for complex constants and taking the dimension to be even: m = 2n, the same set of generators produces the complex Clifford algebra
, which we equip with a Hermitean Clifford conjugation and a Hermitean inner product. Hermitean Clifford analysis then focusses
on the simultaneous null solutions of two mutually conjugate Hermitean Dirac operators, naturally arising in the present context
and being invariant under the action of a realization of the unitary group U (n). In this so–called Hermitean setting Clifford–Hermite polynomials are constructed, starting from a Rodrigues formula involving
both Dirac operators mentioned. Due to the specific features of the Hermitean setting, four different types of polynomials
are obtained, two types of even degree and two types of odd degree. We investigate their properties: recurrence relations,
structure, explicit form and orthogonality w.r.t. a deliberately chosen weight function. They also give rise to the definition
of the Hermitean Clifford–Hermite functions, and may be used to develop a Hermitean continuous wavelet transform, see [4]. 相似文献
12.
Natural bounded concentrators 总被引:1,自引:0,他引:1
Moshe Morgenstern 《Combinatorica》1995,15(1):111-122
We give the first known direct construction for linear families of bounded concentrators. The construction is explicit and
the results are simple natural bounded concentrators.
Let
be the field withq elements,g(x)∈F
q
[x] of degree greater than or equal to 2,
and
. LetI
nputs=H/A,O
utputs=H/B, and draw an edge betweenaA andbB iffaA∩bB≠ϕ. We prove that for everyq≥5 this graph is an
concentrator.
Part of this research was done while the author was at the department of Computer Science, The University of British Columbia,
Vancouver, B.C., Canada. 相似文献
13.
Moshe Dubiner 《Journal d'Analyse Mathématique》1995,67(1):39-116
We consider the problem of polynomial approximation to a real valued functionf defined on a compact set
. An approximation theorem is proven in terms of the newly defined modulus of approximation. It is shown to imply a multidimensional
Jackson type theorem which is stronger than previously known results even for the interval [−1, 1]. A strong multidimensional
Bernstein type inverse theorem is also proven. We allow quite general approximation quasi-norms including
for 0<q≤∞.
We have found that the space of polynomials ℙ on a compact setX induces a semimetric
which encapsulates the local structure of ℙ. Any semimetric ρ equivalent to
suffices for the rough theory presented here. Many examples of sets
and their metrics are presented. 相似文献
14.
By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria and study the
asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation
15.
Zhao Hui HUO Bo Ling GUO 《数学学报(英文版)》2005,21(5):1191-1196
The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local well- posedness is obtained for data in H^s(R)(s 〉 -3/4). For k = 2, local result for data in H^S(R)(s 〉1/4) is obtained. For k = 3, local result for data in H^S(R)(s 〉 -1/6) is obtained. Moreover, the solutions of generalized Korteweg-de Vries-Benjamin-Ono equation converge to the solutions of KdV equation if the term of Benjamin-Ono equation tends to zero. 相似文献
16.
S. Norvidas 《Lithuanian Mathematical Journal》2006,46(4):446-458
Let, for σ > 0,
be the set of complex functions f ∈ L
1 (ℝ) with the Fourier transforms
vanishing outside the interval [−σ; σ]. In this paper, we study the problem of the best approximation of the Dirac function δ (which has the Fourier transform with widest support supp
) by functions
. More precisely, we consider the quantity inf
and its extremal functions
.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 548–564, October–December, 2006. 相似文献
17.
Hoai-Minh Nguyen 《Journal d'Analyse Mathématique》2007,101(1):367-395
In this paper, we prove the estimate
18.
We prove that the maximal Fej'er operator is not bounded on the real Hardy spaces H
1, which may be considered over
and
. We also draw corollaries for the corresponding Hardy spaces over
2 and
2.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
19.
Kamran Divaani-Aazar 《Proceedings Mathematical Sciences》2009,119(1):23-35
Let R be a (not necessarily local) Noetherian ring and M a finitely generated R-module of finite dimension d. Let be an ideal of R and denote the intersection of all prime ideals . It is shown that
20.
Xi Mei WU Qin YUE 《数学学报(英文版)》2007,23(11):2061-2068
Let F = Q(√-p1p2) be an imaginary quadratic field with distinct primes p1 = p2 = 1 mod 8 and the Legendre symbol (p1/p2) = 1. Then the 8-rank of the class group of F is equal to 2 if and only Pl if the following conditions hold: (1) The quartic residue symbols (p1/p2)4 = (p2/p1)4 = 1; (2) Either both
p1 and p2 are represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=x^2-2p1y^2,x,y∈Z,or both p1 and p2 are not represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=ε(2x^2-p1y^2),x,y∈Z,ε∈{±1},where h+(2p1) is the narrow class number of Q(√2p1),Moreover, we also generalize these results. 相似文献
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