共查询到20条相似文献,搜索用时 31 毫秒
1.
We investigate the equiconvergence on TN = [?π, π)N of expansions in multiple trigonometric Fourier series and in the Fourier integrals of functions f ∈ Lp(TN) and g ∈ Lp(RN), p > 1, N ≥ 3, g(x) = f(x) on TN, in the case where the “partial sums” of these expansions, i.e., Sn(x; f) and Jα(x; g), respectively, have “numbers” n ∈ ZN and α ∈ RN (nj = [αj], j = 1,..., N, [t] is the integral part of t ∈ R1) containing N ? 1 components which are elements of “lacunary sequences.” 相似文献
2.
Michael T. Lacey 《Israel Journal of Mathematics》2017,217(1):181-195
A martingale transform T, applied to an integrable locally supported function f, is pointwise dominated by a positive sparse operator applied to |f|, the choice of sparse operator being a function of T and f. As a corollary, one derives the sharp A p bounds for martingale transforms, recently proved by Thiele-Treil-Volberg, as well as a number of new sharp weighted inequalities for martingale transforms. The (very easy) method of proof (a) only depends upon the weak-L 1 norm of maximal truncations of martingale transforms, (b) applies in the vector valued setting, and (c) has an extension to the continuous case, giving a new elementary proof of the A 2 bounds in that setting. 相似文献
3.
Chen Meiri 《Israel Journal of Mathematics》2017,219(2):903-916
Let O(f, ?) be the integral orthogonal group of an integral quadratic form f of signature (n, 1). Let R(f, ?) be the subgroup of O(f, ?) generated by all hyperbolic reflections. Vinberg [Vi3] proved that if n ≥ 30 then the reflective quotient O(f, ?)/R(f, ?) is infinite. In this note we generalize Vinberg’s theorem and prove that if n ≥ 92 then O(f, ?)/R(f, ?) contains a non-abelian free group (and thus it is not amenable). 相似文献
4.
Let M~n(n ≥ 4) be an oriented closed submanifold with parallel mean curvature in an(n + p)-dimensional locally symmetric Riemannian manifold N~(n+p). We prove that if the sectional curvature of N is positively pinched in [δ, 1], and the Ricci curvature of M satisfies a pinching condition, then M is either a totally umbilical submanifold, or δ = 1, and N is of constant curvature. This result generalizes the geometric rigidity theorem due to Xu and Gu[15]. 相似文献
5.
V. Z. Grines E. Ya. Gurevich V. S. Medvedev 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):59-83
Let M n be a closed orientable manifold of dimension greater than three and G 1(M n ) be the class of orientation-preserving Morse-Smale diffeomorphisms on M n such that the set of unstable separatrices of every f ∈ G 1(M n ) is one-dimensional and does not contain heteroclinic orbits. We show that the Peixoto graph is a complete invariant of topological conjugacy in G 1(M n ). 相似文献
6.
Let M be a subharmonic function with Riesz measure ν M in a domain D in the n-dimensional complex Euclidean space ? n , and let f be a nonzero function that is holomorphic in D, vanishes on a set Z ? D, and satisfies |f| ? expM on D. Then restrictions on the growth of ν M near the boundary of D imply certain restrictions on the dimensions or the area/volume of Z. We give a quantitative study of this phenomenon in the subharmonic framework. 相似文献
7.
W. R. Lü F. Lü L. Wu J. Yang 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2018,53(5):260-265
In this note, we study the admissible meromorphic solutions for algebraic differential equation fnf' + Pn?1(f) = R(z)eα(z), where Pn?1(f) is a differential polynomial in f of degree ≤ n ? 1 with small function coefficients, R is a non-vanishing small function of f, and α is an entire function. We show that this equation does not possess any meromorphic solution f(z) satisfying N(r, f) = S(r, f) unless Pn?1(f) ≡ 0. Using this result, we generalize a well-known result by Hayman. 相似文献
8.
Let M be an n-dimensional complete Riemannian manifold with Ricci curvature n- 1. By developing some new techniques, Colding(1996) proved that the following three conditions are equivalent: 1)dGH(M, S~n) → 0; 2) the volume of M Vol(M) → Vol(S~n); 3) the radius of M rad(M) →π. By developing a different technique, Petersen(1999) gave the 4th equivalent condition, namely he proved that the n + 1-th eigenvalue of M, λ_(n+1)(M) → n, is also equivalent to the radius of M, rad(M) →π, and hence the other two.In this paper, we use Colding's techniques to give a new proof of Petersen's theorem. We expect our estimates will have further applications. 相似文献
9.
Ricardo Abreu-Blaya Juan Bory-Reyes Jean-Marie Vilaire 《Complex Analysis and Operator Theory》2010,4(2):133-143
This paper is devoted to the compactness of the hypercomplex commutator S γ M a ? M a S γ, where S γ is the Cauchy singular integral operator (in the Douglis sense), a is a Hölder continuous hypercomplex function and M a is the multiplication operator given by M a f = a f. We extend a known compactness sufficient condition for the commutator of the Cauchy singular integral operator to the frame of the hypercomplex analysis, where γ is merely required to be an arbitrary regular closed Jordan curve. 相似文献
10.
An arithmetic function f is called a sieve function of range Q if its Eratosthenes transform g = f * μ is supported in [1,Q] ∩ N, where g(q) ? ε q ε (?ε > 0). We continue our study of the distribution of f(n) over short arithmetic bands, n ≡ ar + b (mod q), with n ∈ (N,2N] ∩ N, 1 ≤ a ≤ H = o(N) and r,b ∈ Z such that g:c:d:(r,q) = 1. In particular, the optimality of some results is discussed. 相似文献
11.
12.
Let G be a finite group. If Mn< Mn?1< · · · < M1< M0 = G with Mi a maximal subgroup of Mi?1 for all i = 1,..., n, then Mn (n > 0) is an n-maximal subgroup of G. A subgroup M of G is called modular provided that (i) 〈X,M ∩ Z〉 = 〈X,M〉 ∩ Z for all X ≤ G and Z ≤ G such that X ≤ Z, and (ii) 〈M,Y ∩ Z〉 = 〈M,Y 〉 ∩ Z for all Y ≤ G and Z ≤ G such that M ≤ Z. In this paper, we study finite groups whose n-maximal subgroups are modular. 相似文献
13.
Hong Huang 《Annals of Global Analysis and Geometry》2009,36(3):323-325
In this note, we prove the following result. There is a positive constant ε(n, Λ) such that if M n is a simply connected compact Kähler manifold with sectional curvature bounded from above by Λ, diameter bounded from above by 1, and with holomorphic bisectional curvature H ≥ ?ε(n, Λ), then M n is diffeomorphic to the product M 1 × ? × M k , where each M i is either a complex projective space or an irreducible Kähler–Hermitian symmetric space of rank ≥ 2. This resolves a conjecture of Fang under the additional upper bound restrictions on sectional curvature and diameter. 相似文献
14.
Jerzy Jezierski 《中国科学 数学(英文版)》2017,60(9):1579-1590
There are two algebraic lower bounds of the number of n-periodic points of a self-map f : M → M of a compact smooth manifold of dimension at least 3: NF_n(f) = min{#Fix(g~n); g ~ f; g continuous} and NJD_n(f) = min{#Fix(g~n); g ~ f; g smooth}. In general, NJD_n(f) may be much greater than NF_n(f). We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism,the equality NF_n(f) = NJD_n(f) holds for all n ? all eigenvalues of a quotient cohomology homomorphism induced by f have moduli 1. 相似文献
15.
D. V. Zakablukov 《Moscow University Mathematics Bulletin》2016,71(3):89-97
The paper discusses the asymptotic depth of a reversible circuits consisting of NOT, CNOT and 2-CNOT gates. The reversible circuit depth function D(n, q) is introduced for a circuit implementing a mapping f: Z2n → Z2n as a function of n and the number q of additional inputs. It is proved that for the case of implementation of a permutation from A(Z2n) with a reversible circuit having no additional inputs the depth is bounded as D(n, 0) ? 2n/(3log2n). It is also proved that for the case of transformation f: Z2n → Z2n with a reversible circuit having q0 ~ 2n additional inputs the depth is bounded as D(n,q0) ? 3n. 相似文献
16.
A subposet Q ′ of a poset Q is a copy of a poset P if there is a bijection f between elements of P and Q ′ such that x ≤ y in P iff f(x) ≤ f(y) in Q. For posets P, P ′, let the poset Ramsey number R(P, P ′) be the smallest N such that no matter how the elements of the Boolean lattice Q N are colored red and blue, there is a copy of P with all red elements or a copy of P ′ with all blue elements. We provide some general bounds on R(P, P ′) and focus on the situation when P and P ′ are both Boolean lattices. In addition, we give asymptotically tight bounds for the number of copies of Q n in Q N and for a multicolor version of a poset Ramsey number. 相似文献
17.
Consider the second order discrete Hamiltonian systems Δ2u(n-1)-L(n)u(n) + ▽W (n, u(n)) = f(n),where n ∈ Z, u ∈ RN and W : Z × RN → R and f : Z → RN are not necessarily periodic in n. Under some comparatively general assumptions on L, W and f , we establish results on the existence of homoclinic orbits. The obtained results successfully generalize those for the scalar case. 相似文献
18.
Any analytic signal fa(e~(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition, Kumarasan and Rao(1999), implementing the idea of the Szeg?o limit theorem(see below),proposed an algorithm to obtain approximations of the minimum-phase signal of a polynomial analytic signal fa(e~(it)) = e~(iN0t)M∑k=0a_k~(eikt),(0.1)where a_0≠ 0, a_M≠ 0. Their method involves minimizing the energy E(f_a, h_1, h_2,..., h_H) =1/(2π)∫_0~(2π)|1+H∑k=1h_k~(eikt)|~2|fa(e~(it))|~2dt(0.2) with the undetermined complex numbers hk's by the least mean square error method. In the limiting procedure H →∞, one obtains approximate solutions of the minimum-phase signal. What is achieved in the present paper is two-fold. On one hand, we rigorously prove that, if fa(e~(it)) is a polynomial analytic signal as given in(0.1),then for any integer H≥M, and with |fa(e~(it))|~2 in the integrand part of(0.2) being replaced with 1/|fa(e~(it))|~2,the exact solution of the minimum-phase signal of fa(e~(it)) can be extracted out. On the other hand, we show that the Fourier system e~(ikt) used in the above process may be replaced with the Takenaka-Malmquist(TM) system, r_k(e~(it)) :=((1-|α_k|~2e~(it))/(1-α_ke~(it))~(1/2)∏_(j=1)~(k-1)(e~(it)-α_j/(1-α_je~(it))~(1/2), k = 1, 2,..., r_0(e~(it)) = 1, i.e., the least mean square error method based on the TM system can also be used to extract out approximate solutions of minimum-phase signals for any functions f_a in the Hardy space. The advantage of the TM system method is that the parameters α_1,..., α_n,...determining the system can be adaptively selected in order to increase computational efficiency. In particular,adopting the n-best rational(Blaschke form) approximation selection for the n-tuple {α_1,..., α_n}, n≥N, where N is the degree of the given rational analytic signal, the minimum-phase part of a rational analytic signal can be accurately and efficiently extracted out. 相似文献
19.
RAMESH KASILINGAM 《Proceedings Mathematical Sciences》2016,126(2):277-281
We classify, up to diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective n-space \(\mathbb {C}\textbf {P}^{n}\), where n=3 and 4. Let M2n be a closed smooth 2n-manifold homotopy equivalent to \(\mathbb {C}\textbf {P}^{n}\). We show that, up to diffeomorphism, M6 has a unique differentiable structure and M8 has at most two distinct differentiable structures. We also show that, up to concordance, there exist at least two distinct differentiable structures on a finite sheeted cover N2n of \(\mathbb {C}\textbf {P}^{n}\) for n=4,7 or 8 and six distinct differentiable structures on N10. 相似文献
20.
For X, Y ∈ Mn,m it is said that X is gut-majorized by Y, and we write X ?gutY, if there exists an n-by-n upper triangular g-row stochastic matrix R such that X = RY. Define the relation ~gut as follows. X ~gutY if X is gut-majorized by Y and Y is gut-majorized by X. The (strong) linear preservers of ?gut on ?n and strong linear preservers of this relation on Mn,m have been characterized before. This paper characterizes all (strong) linear preservers and strong linear preservers of ~gut on ?n and Mn,m. 相似文献