共查询到20条相似文献,搜索用时 604 毫秒
1.
V. A. Belonogov 《Proceedings of the Steklov Institute of Mathematics》2013,283(1):6-23
Previously, the author made the following conjecture: if a finite group has two semiproportional irreducible characters φ and ψ, then φ(1) = ψ(1). In the present paper, a new confirmation of the conjecture is obtained. Namely, the conjecture is verified for symplectic groups Sp4(q) and PSp4(q). 相似文献
2.
Y. Q. Yan 《Functional Analysis and Its Applications》2005,39(4):321-323
Let φ be an N-function. Then the normal structure coefficients N and the weakly convergent sequence coefficients WCS of the Orlicz function spaces L φ[0, 1] generated by φ and equipped with the Luxemburg and Orlicz norms have the following exact values. (i) If F φ(t) = t ?(t)/φ(t) is decreasing and 1 < C φ < 2 (where \(C_\Phi = \lim _{t \to + \infty } t\varphi (t)/\Phi (t)\)), then N(L (φ)[0, 1]) = N(L φ[0, 1]) = WCS(L (φ)[0, 1]) = WCS(L φ[0, 1]) = 21?1/Cφ. (ii) If F φ(t) is increasing and C φ > 2, then N(L (φ)[0, 1]) = N(L φ[0, 1]) = WCS(L (φ)[0, 1]) = WCS(L φ[0, 1]) = 21/Cφ. 相似文献
3.
David Kalaj 《Israel Journal of Mathematics》2017,218(1):67-81
Assume that (N, ?) and (M, S) are two Riemann surfaces with conformal metrics ? and S. We prove that if there is a harmonic homeomorphism between an annulus A ? N with a conformal modulus Mod(A) and a geodesic annulus A S (p, ρ1, ρ2)?M, then we have ρ2/ρ1 ≥ Ψ S Mod(A)2+ 1, where Ψ S is a certain positive constant depending on the upper bound of Gaussian curvature of the metric S. An application for the minimal surfaces is given. 相似文献
4.
Schrödinger operators with infinite-rank singular potentials V=Σ i,j=1 ∞ b ij〈φj,·〉φi are studied under the condition that the singular elements ψ j are ξ j(t)-invariant with respect to scaling transformationsin ?3. 相似文献
5.
A. A. Illarionov 《Proceedings of the Steklov Institute of Mathematics》2017,299(1):96-108
Functional equations of the form f(x + y)g(x ? y) = Σ j=1 n α j (x)β j (y) as well as of the form f1(x + z)f2(y + z)f3(x + y ? z) = Σ j=1 m φ j (x, y)ψ j (z) are solved for unknown entire functions f, g,α j , β j : ? → ? and f1, f2, f3, ψ j : ? → ?, φ j : ?2 → ? in the cases of n = 3 and m = 4. 相似文献
6.
F. M. Korkmasov 《Vestnik St. Petersburg University: Mathematics》2007,40(2):138-151
It is shown that if P m α,β (x) (α, β > ?1, m = 0, 1, 2, …) are the classical Jaboci polynomials, then the system of polynomials of two variables {Ψ mn α,β (x, y)} m,n=0 r = {P m α,β (x)P n α,β (y)} m, n=0 r (r = m + n ≤ N ? 1) is an orthogonal system on the set Ω N×N = ?ub;(x i , y i ) i,j=0 N , where x i and y i are the zeros of the Jacobi polynomial P n α,β (x). Given an arbitrary continuous function f(x, y) on the square [?1, 1]2, we construct the discrete partial Fourier-Jacobi sums of the rectangular type S m, n, N α,β (f; x, y) by the orthogonal system introduced above. We prove that the order of the Lebesgue constants ∥S m, n, N α,β ∥ of the discrete sums S m, n, N α,β (f; x, y) for ?1/2 < α, β < 1/2, m + n ≤ N ? 1 is O((mn) q + 1/2), where q = max?ub;α,β?ub;. As a consequence of this result, several approximate properties of the discrete sums S m, n, N α,β (f; x, y) are considered. 相似文献
7.
Let (X, μ) and (Y, ν) be standard measure spaces. A function \({\varphi\in L^\infty(X\times Y,\mu\times\nu)}\) is called a (measurable) Schur multiplier if the map S φ , defined on the space of Hilbert-Schmidt operators from L 2(X, μ) to L 2(Y, ν) by multiplying their integral kernels by φ, is bounded in the operator norm. The paper studies measurable functions φ for which S φ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if φ is of Toeplitz type, that is, if φ(x, y) = f(x ? y), \({x,y\in G}\), where G is a locally compact abelian group, then the closability of φ is related to the local inclusion of f in the Fourier algebra A(G) of G. If φ is a divided difference, that is, a function of the form (f(x) ? f(y))/(x ? y), then its closability is related to the “operator smoothness” of the function f. A number of examples of non-closable, norm closable and w*-closable multipliers are presented. 相似文献
8.
Zong Xiju Zhao Yi Yin Zhaoyang Chi Tao 《高校应用数学学报(英文版)》2007,22(3):277-285
In this paper, the boundary control problem of a distributed parameter system described by the Schr(o)dinger equation posed on finite interval α≤ x ≤β:{iyt yxx |y|2y = 0,y(α,t) = h1(t),y(β,t) = h2(t) for t > 0 (S)is considered. It is shown that by choosing appropriate control inputs (hj), (j = 1,2) one can always guide the system (S) from a given initial state ψ∈ Hs(α,β),(s ∈ R) to a terminal state ψ∈ Hs(α,β), in the time period [0, T]. The exact boundary controllability is obtained by considering a related initial value control problem of Schr(o)dinger equation posed on the whole line R. The discovered smoothing properties of Schr(o)dinger equation have played important roles in our approach; this may be the first step to prove the results on boundary controllability of (semi-linear) nonlinear Schr(o)dinger equation. 相似文献
9.
We consider the boundedness of the rough singular integral operator T_(?,ψ,h) along a surface of revolution on the Triebel-Lizorkin space F~α_( p,q)(R~n) for ? ∈ H~1(~(Sn-1)) and ? ∈ Llog~+L(S~(n-1)) ∪_1q∞(B~((0,0))_q(S~(n-1))), respectively. 相似文献
10.
Denote the set of all holomorphic mappings of a genus 3 Riemann surface S 3 onto a genus 2 Riemann surface S 2 by Hol(S 3, S 2). Call two mappings f and g in Hol(S 3, S 2) equivalent whenever there exist conformal automorphisms α and β of S 3 and S 2 respectively with f ? α = β ? g. It is known that Hol(S 3, S 2) always consists of at most two equivalence classes.We obtain the following results: If Hol(S 3, S 2) consists of two equivalence classes then both S 3 and S 2 can be defined by real algebraic equations; furthermore, for every pair of inequivalent mappings f and g in Hol(S 3, S 2) there exist anticonformal automorphisms α? and β? with f ? α? = β? ? g. Up to conformal equivalence, there exist exactly three pairs of Riemann surfaces (S 3, S 2) such that Hol(S 3, S 2) consists of two equivalence classes. 相似文献
11.
A. A. Makhnev M. S. Nirova 《Proceedings of the Steklov Institute of Mathematics》2007,257(1):S135-S144
A geometry of rank 2 is an incidence system (P, \(\mathcal{B}\)), where P is a set of points and \(\mathcal{B}\) is a set of subsets from P, called blocks. Two points are called collinear if they lie in a common block. A pair (a, B) from (P, \(\mathcal{B}\)) is called a flag if its point belongs to the block, and an antiflag otherwise. A geometry is called φ-uniform (φ is a natural number) if for any antiflag (a, B) the number of points in the block B collinear to the point a equals 0 or φ, and strongly φ-uniform if this number equals φ. In this paper, we study φ-uniform extensions of partial geometries pG α (s, t) with φ = s and strongly φ-uniform geometries with φ = s ? 1. In particular, the results on extensions of generalized quadrangles, obtained earlier by Cameron and Fisher, are extended to the case of partial geometries. 相似文献
12.
N. L. Grigorenko D. V. Kamzolkin L. N. Luk’yanova 《Proceedings of the Steklov Institute of Mathematics》2011,273(1):49-58
Let {φ n (α,β) (z)} n=0 ∞ be a system of Jacobi polynomials orthonormal on the circle |z| = 1 with respect to the weight (1 ? cos τ)α+1/2(1 + cos τ)β+1/2 (α, β > ?1), and let \(\psi _n^{\left( {\alpha ,\beta } \right)*} \left( z \right): = z^n \overline {\psi _n^{\left( {\alpha ,\beta } \right)} \left( {{1 \mathord{\left/ {\vphantom {1 {\bar z}}} \right. \kern-\nulldelimiterspace} {\bar z}}} \right)}\)). We establish relations between the polynomial φ n (α,?1/2) (z) and the nth (C, α ? 1/2)-mean of the Maclaurin series for the function (1 ? z)?α?3/2 and also between the polynomial φ n (α,?1/2)* (z) and the nth (C, α + 1/2)-mean of the Maclaurin series for the function (1 ? z)?α?1/2. We use these relations to derive an asymptotic formula for φ n (α,?1/2) (z); the formula is uniform inside the disk |z| < 1. It follows that φ n (α,?1/2) (z) ≠ 0 in the disk |z| ≤ ρ for fixed φ ∈ (0, 1) and α > ?1 if n is sufficiently large. 相似文献
13.
A. I. Petrosyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2017,52(6):295-304
The paper studies the Banach spaces h ∞(φ), h 0(φ), and h 1(η) of harmonic functions over the unit ball in R n . These spaces depend on a weight function φ and a weight measure η. For a given function φ from a sufficiently broad class of functions, we solve the duality problem. that is, we construct measures η such that h 1(η)* ~ h ∞(φ) and h 0(φ)* ~ h 1(η). 相似文献
14.
We find the greatest value α 1 and α 2, and the least values β 1 and β 2, such that the double inequalities α 1 S(a,b)?+?(1???α 1) A(a,b)?T(a,b)?β 1 S(a,b)?+?(1???β 1) A(a,b) and \(S^{\alpha_{2}}(a,b)A^{1-\alpha_{2}}(a,b)< T(a,b)< S^{\beta_{2}}(a,b)A^{1-\beta_{2}}(a,b)\) hold for all a,b?>?0 with a?≠?b. As applications, we get two new bounds for the complete elliptic integral of the second kind in terms of elementary functions. Here, S(a,b)?=?[(a 2?+?b 2)/2]1/2, A(a,b)?=?(a?+?b)/2, and \(T(a,b)=\frac{2}{\pi}\int\limits_{0}^{{\pi}/{2}}\sqrt{a^2{\cos^2{\theta}}+b^2{\sin^2{\theta}}}{\rm d}\theta\) denote the root-square, arithmetic, and Toader means of two positive numbers a and b, respectively. 相似文献
15.
V. A. Bykovskii 《Doklady Mathematics》2016,94(2):527-528
Given any nonzero entire function g: ? → ?, the complex linear space F(g) consists of all entire functions f decomposable as f(z + w)g(z - w)=φ1(z)ψ1(w)+???+ φn(z)ψn(w) for some φ1, ψ1, …, φn, ψn: ? → ?. The rank of f with respect to g is defined as the minimum integer n for which such a decomposition is possible. It is proved that if g is an odd function, then the rank any function in F(g) is even. 相似文献
16.
Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk \(\mathbb{D}\) in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators uC φ from Zygmund type spaces to Bloch type spaces in \(\mathbb{D}\) in terms of u, φ, their derivatives, and φ n , the n-th power of φ. Moreover, we obtain some similar estimates for the essential norms of the operators uC φ , from which sufficient and necessary conditions of compactness of uC φ follows immediately. 相似文献
17.
Let φ 1 and φ 2 be holomorphic self-maps of the unit polydisk \(\mathbb{D}^N\), and let u 1 and u 2 be holomorphic functions on \(\mathbb{D}^N\). We characterize the boundedness and compactness of the difference of weighted composition operators W φ1, u1 and W φ2, u2 from the weighted Bergman space \(A_{\vec \alpha }^p\), 0 < p < ∞, \(\vec \alpha = \left( {\alpha _1 , \ldots ,\alpha _{\rm N} } \right)\), α j > ?1, j = 1,..., N, to the weighted-type space H υ ∞ of holomorphic functions on the unit polydisk \(\mathbb{D}^N\) in terms of inducing symbols φ 1, φ 2, u 1, and u 2. 相似文献
18.
FuQuan Fang 《中国科学 数学(英文版)》2017,60(9):1549-1560
Let Σ be a simply connected rational homology sphere. A pair of disjoint closed submanifolds M_+, M_-? Σ are called dual to each other if the complement Σ-M_+ strongly homotopy retracts onto M_- or vice-versa. In this paper, we are concerned with the basic problem of which integral triples(n; m_+, m-) ∈ N~3 can appear, where n = dimΣ-1 and m_± = codim M_±-1. The problem is motivated by several fundamental aspects in differential geometry.(i) The theory of isoparametric/Dupin hypersurfaces in the unit sphere S~(n+1) initiated by′Elie Cartan, where M_± are the focal manifolds of the isoparametric/Dupin hypersurface M ? S~(n+1), and m± coincide with the multiplicities of principal curvatures of M.(ii) The Grove-Ziller construction of non-negatively curved Riemannian metrics on the Milnor exotic spheres Σ,i.e., total spaces of smooth S~3-bundles over S~4 homeomorphic but not diffeomorphic to S~7, where M_± =P_±×_(SO(4))S~3, P → S~4 the principal SO(4)-bundle of Σ and P_± the singular orbits of a cohomogeneity one SO(4) × SO(3)-action on P which are both of codimension 2.Based on the important result of Grove-Halperin, we provide a surprisingly simple answer, namely, if and only if one of the following holds true:· m_+ = m_-= n;· m_+ = m_-=1/3n ∈ {1, 2, 4, 8};· m_+ = m_-=1/4n ∈ {1, 2};· m_+ = m_-=1/6n ∈ {1, 2};·n/(m_++m_-)= 1 or 2, and for the latter case, m_+ + m_-is odd if min(m_+, m_-)≥2.In addition, if Σ is a homotopy sphere and the ratio n/(m_++m_-)= 2(for simplicity let us assume 2 m_- m_+),we observe that the work of Stolz on the multiplicities of isoparametric hypersurfaces applies almost identically to conclude that, the pair can be realized if and only if, either(m_+, m_-) =(5, 4) or m_+ + m_-+ 1 is divisible by the integer δ(m_-)(see the table on Page 1551), which is equivalent to the existence of(m_--1) linearly independent vector fields on the sphere S~(m_++m_-)by Adams' celebrated work. In contrast, infinitely many counterexamples are given if Σ is a rational homology sphere. 相似文献
19.
M. G. Grigoryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(4):205-218
Let χ = {χ n } n=0 ∞ be the Haar system normalized in L 2(0, 1) and M = {M s } s=1 ∞ be an arbitrary, increasing sequence of nonnegative integers. For any subsystem of χ of the form {φ k } = χS = {χ n } n∈S , where S = S(M) = {n k } k=1 ∞ = {n ∈ V[p]: p ∈ M}, V[0] = {1, 2} and V[p] = {2 p + 1, 2 p + 2, …, 2 p+1} for p = 1, 2, … a series of the form Σ i=1 ∞ a i φ i with a i ↘ 0 is constructed, that is universal with respect to partial series in all classes L r (0, 1), r ∈ (0, 1), in the sense of a.e. convergence and in the metric ofL r (0, 1). The constructed series is universal in the class of all measurable, finite functions on [0, 1] in the sense of a.e. convergence. It is proved that there exists a series by Haar system with decreasing coefficients, which has the following property: for any ? > 0 there exists a measurable function µ(x), x ∈ [0, 1], such that 0 ≤ µ(x) ≤ 1 and |{x ∈ [0, 1], µ(x) ≠ = 1}| < ?, and the series is universal in the weighted space L µ[0, 1] with respect to subseries, in the sense of convergence in the norm of L µ[0, 1]. 相似文献
20.
Let θ ∈ (0, 1), λ ∈ [0, 1) and p, p 0, p 1 ∈ (1,∞] be such that (1 ? θ)/p 0 + θ/p 1 = 1/p, and let φ, φ0, φ1 be some admissible functions such that φ, φ0 p/p0 and φ1 p/p1 are equivalent. We first prove that, via the ± interpolation method, the interpolation L φ0 p0),λ (X), L φ1 p1), λ (X), θ> of two generalized grand Morrey spaces on a quasi-metric measure space X is the generalized grand Morrey space L φ p),λ (X). Then, by using block functions, we also find a predual space of the generalized grand Morrey space. These results are new even for generalized grand Lebesgue spaces. 相似文献