共查询到20条相似文献,搜索用时 578 毫秒
1.
B. B. Tsegaw 《Differential Equations》2015,51(12):1607-1619
We study the nonexistence of weak solutions of higher-order elliptic and parabolic inequalities of the following types: \(\sum {_{i = 1}^N\sum\nolimits_{{e_i} \leqslant {\alpha _i} \leqslant {m_i}} {D_{{x_i}}^{{\alpha _i}}\left( {{A_{{\alpha _i}}}\left( {x,u} \right)} \right)} \geqslant f\left( {x,u} \right),} x \in {\mathbb{R}^N}\), and \({u_t} + \sum {_{i = 1}^N\sum\nolimits_{{k_i} \leqslant {\beta _i} \leqslant {n_i}} {D_{{x_i}}^{{\beta _i}}\left( {{B_{{\beta _i}}}\left( {x,t,u} \right)} \right)} > g\left( {x,t,u} \right),\left( {x,t} \right)} \in {\mathbb{R}^N} \times {\mathbb{R}_ + }\), where l i , m i , k i , n i ∈ N satisfy the condition l i , k i > 1 for all i = 1,..., N, and A αi (x, u), B βi (x, t, u), f(x, u), and g(x, t, u) are some given Carathéodory functions. Under appropriate conditions on the functions A αi , B βi , f, and g, we prove theorems on the nonexistence of solutions of these inequalities. 相似文献
2.
M. A. Korolev 《Proceedings of the Steklov Institute of Mathematics》2017,296(1):154-171
The work is devoted to generalized Kloosterman sums modulo a prime, i.e., trigonometric sums of the form \(\sum\nolimits_{p \leqslant x} {\exp \left\{ {2\pi i\left( {a\bar p + {F_k}\left( p \right)} \right)/q} \right\}} \) and \(\sum\nolimits_{n \leqslant x} {\mu \left( n \right)\exp \left\{ {2\pi i\left( {a\bar n + {F_k}\left( n \right)} \right)/q} \right\}} \), where q is a prime number, \(\left( {a,q} \right) = 1,m\bar m \equiv 1\left( {\bmod {\kern 1pt} q} \right)\), F k (u) is a polynomial of degree k ≥ 2 with integer coefficients, and p runs over prime numbers. An upper estimate with a power saving is obtained for the absolute values of such sums for x ≥ q1/2+ε. 相似文献
3.
Let n ≥ 3. The complex Lie algebra, which is attached to a unit form q(x 1, x 2,..., x n) = \({\sum\nolimits_{i = 1}^n {x_i^2 + \sum\nolimits_{1 \leqslant i \leqslant j \leqslant n} {\left( { - 1} \right)} } ^{j - i}}{x_i}{x_j}\) and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A n , and realized by the Ringel-Hall Lie algebra of a Nakayama algebra of radical square zero. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra. 相似文献
4.
A remark on the existence of entire large and bounded solutions to a (<Emphasis Type="Italic">k</Emphasis><Subscript>1</Subscript>, <Emphasis Type="Italic">k</Emphasis><Subscript>2</Subscript>)-Hessian system with gradient term 下载免费PDF全文
Dragos Patru Covei 《数学学报(英文版)》2017,33(6):761-774
In this paper, we study the existence of positive entire large and bounded radial positive solutions for the following nonlinear system Here \({S_{{k_i}}}\left( {\lambda \left( {{D^2}{u_i}} \right)} \right)\) is the k i -Hessian operator, a 1, p 1, f 1, a 2, p 2 and f 2 are continuous functions.
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$$\left\{ {\begin{array}{*{20}c}{S_{k_1 } \left( {\lambda \left( {D^2 u_1 } \right)} \right) + a_1 \left( {\left| x \right|} \right)\left| {\nabla u_1 } \right|^{k_1 } = p_1 \left( {\left| x \right|} \right)f_1 \left( {u_2 } \right)} & {for x \in \mathbb{R}^N ,} \\{S_{k_2 } \left( {\lambda \left( {D^2 u_2 } \right)} \right) + a_2 \left( {\left| x \right|} \right)\left| {\nabla u_2 } \right|^{k_2 } = p_2 \left( {\left| x \right|} \right)f_2 \left( {u_1 } \right)} & {for x \in \mathbb{R}^N .} \\\end{array} } \right.$$
5.
Let \({\{ {f_{\lambda ;j}}\} _{\lambda \in V;1 \leqslant j \leqslant k}}\) be families of holomorphic functions in the open unit disk \({\text{D}} \subset {\Bbb C}\) ? ? depending holomorphically on a parameter λ ∈ V ? ? n . We establish a Rolle type theorem for the generalized multiplicity (called cyclicity) of zeros of the family of univariate holomorphic functions \({\left\{ {\sum\nolimits_{j = 1}^k {{f_{\lambda ;j}}} } \right\}_{\lambda \in V}}\) at 0 ∈ D. As a corollary, we estimate the cyclicity of the family of generalized exponential polynomials, that is, the family of entire functions of the form \(\sum\nolimits_{k = 1}^m {{P_k}(z){e^{{Q_k}(z)}}} \), z ∈ ?, where P k and Q k are holomorphic polynomials of degrees p and q, respectively, parameterized by vectors of coefficients of P k and Q k . 相似文献
6.
In this paper,a uniqueness theorem for meromorphic mappings partially sharing 2N+3 hyperplanes is proved.For a meromorphic mapping f and a hyperplane H,set E(H,f) = {z|ν(f,H)(z) 0}.Let f and g be two linearly non-degenerate meromorphic mappings and {Hj}j2=N1+ 3be 2N + 3 hyperplanes in general position such that dim f-1(Hi) ∩ f-1(Hj) n-2 for i = j.Assume that E(Hj,f) E(Hj,g) for each j with 1 j 2N +3 and f = g on j2=N1+ 3f-1(Hj).If liminfr→+∞ 2j=N1+ 3N(1f,Hj)(r) j2=N1+ 3N(1g,Hj)(r) NN+1,then f ≡ g. 相似文献
7.
Let f and g be multiplicative functions of modulus 1. Assume that \( {\lim_{x \to \infty }}\frac{1}{x}\left| {\sum\nolimits_{n \leqslant x} {f(n)} } \right| = A > 0 \) and \( {\lim_{x \to \infty }}\frac{1}{x}\left| {\sum\nolimits_{n \leqslant x} {g(n)} } \right| = 0 \). We prove that, under these conditions,Concerning the Liouville function λ, we find an upper estimate for \( \frac{1}{x}\left| {\sum\limits_{n \leqslant x} {\lambda (n)\lambda (n + 1)} } \right| \) under the unproved hypothesis that L(s, χ) have Siegel zeros for an infinite sequence of L-functions.
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$ \mathop {\lim }\limits_{x \to \infty } \frac{1}{x}\sum\limits_{n \leqslant x} {f(n)g(n + 1) = 0.}$
8.
REN Xiumin Department of Mathematics Shandong University Jinan China 《中国科学A辑(英文版)》2005,48(6):785-797
In this paper, we prove the following estimate on exponential sums over primes: Let κ≥1,βκ=1/2 log κ/log2, x≥2 and α=a/q λsubject to (a, q) = 1, 1≤a≤q, and λ∈R. Then As an application, we prove that with at most O(N2/8 ε) exceptions, all positive integers up to N satisfying some necessary congruence conditions are the sum of three squares of primes. This result is as strong as what has previously been established under the generalized Riemann hypothesis. 相似文献
9.
The paper outlines why the spectrum of maximal ideals Spec ? A of a countable-dimensional differential ?-algebra A of transcendence degree 1 without zero divisors is locally analytic, which means that for any ?-homomorphism ψ M: A → ? (M ∈ Spec ? A) and any a ∈ A the Taylor series \(\widetilde {{\psi _M}}{\left( a \right)^{\underline{\underline {def}} }}\sum\limits_{m = 0}^\infty {\psi M\left( {{a^{\left( m \right)}}} \right)} \frac{{{z^m}}}{{m!}}\) has nonzero radius of convergence depending on the element a ∈ A. 相似文献
10.
S. Gulzar N. A. Rather 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2018,53(1):21-26
The Schur-Szegö composition of two polynomials \(f\left( z \right) = \sum\nolimits_{j = 0}^n {{A_j}{z^j}} \) and \(g\left( z \right) = \sum\nolimits_{j = 0}^n {{B_j}{z^j}} \), both of degree n, is defined by \(f * g\left( z \right) = \sum\nolimits_{j = 0}^n {{A_j}{B_j}{{\left( {\begin{array}{*{20}{c}}n \\ j \end{array}} \right)}^{ - 1}}{z^j}} \). In this paper, we estimate the minimum and the maximum of the modulus of f * g(z) on z = 1 and thereby obtain results analogues to Bernstein type inequalities for polynomials. 相似文献
11.
Qinghua Pi 《Lithuanian Mathematical Journal》2011,51(4):543-561
Let f be a fixed holomorphic Hecke eigen cusp form of weight k for \( SL\left( {2,{\mathbb Z}} \right) \), and let \( {\mathcal U} = \left\{ {{u_j}:j \geqslant 1} \right\} \) be an orthonormal basis of Hecke–Maass cusp forms for \( SL\left( {2,{\mathbb Z}} \right) \). We prove an asymptotic formula for the twisted first moment of the Rankin–Selberg L-functions \( L\left( {s,f \otimes {u_j}} \right) \) at \( s = \frac{1}{2} \) as u j runs over \( {\mathcal U} \). It follows that f is uniquely determined by the central values of the family of Rankin–Selberg L-functions \( \left\{ {L\left( {s,f \otimes {u_j}} \right):{u_j} \in {\mathcal U}} \right\} \). 相似文献
12.
Yu. S. Osipov A. V. Kryazhimskii V. I. Maksimov 《Proceedings of the Steklov Institute of Mathematics》2011,273(1):86-120
For the weight \(v_k \left( x \right) = \prod _{\alpha \in \mathbb{R}_ + } \left| {\left( {\alpha ,x} \right)} \right|^{2k\left( \alpha \right)}\) defined by a positive subsystem R + of a finite root system R ? ? d and by a function k(α): R → ?+ invariant under the reflection group generated by R, a sharp Jackson inequality in L 2(? d ) is proved. 相似文献
13.
K. I. Oskolkov M. A. Chakhkiev 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):186-196
The function \(\psi : = \sum\nolimits_{n \in \mathbb{Z}\backslash \left\{ 0 \right\}} {{{e^{\pi i\left( {tn^2 + 2xn} \right)} } \mathord{\left/ {\vphantom {{e^{\pi i\left( {tn^2 + 2xn} \right)} } {\left( {\pi in^2 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\pi in^2 } \right)}}} \), {t, x} ?2, is studied as a (generalized) solution of the Cauchy initial value problem for the Schrödinger equation. The real part of the restriction of ψ on the line x = 0, that is, the function \(R: = Re\psi \left| {_{x = 0} = \tfrac{2}{n}} \right.\sum\nolimits_{n \in \mathbb{N}} {\frac{{\sin \pi n^2 t}}{{n^2 }}} \), t ∈ ?, was suggested by B. Riemann as a plausible example of a continuous but nowhere differentiable function. The points are established on ?2 where the partial derivative \(\frac{{\partial \psi }}{{\partial t}}\) exists and equals ?1. These points constitute a countable set of open intervals parallel to the x-axis, with rational values of t. Thereby a natural extension of the well-known results of G.H. Hardy and J. Gerver is obtained (Gerver established that the derivative of the function R still does exist and equals ?1 at each rational point of the type \(t = \frac{a}{q}\) where both numbers a and q are odd). A basic role is played by a representation of the differences of the function ψ via Poisson’s summation formula and the oscillatory Fresnel integral. It is also proved that the number 3 4 is the sharp value of the Lipschitz-Hölder exponent of the function ψ in the variable t almost everywhere on ?2. 相似文献
14.
Fixed points of meromorphic functions and of their differences,divided differences and shifts 下载免费PDF全文
Let f(z) be a finite order meromorphic function and let c∈C\{0} be a constant.If f(z)has a Borel exceptional value a∈C,it is proved that max{τ(f(z)),τ(△_cf(z))}=max{τ(f(z)),τ(f(z+c))}=max{τ(△_cf(z)),τ(f(z+c))}=σ(f(z)).If f(z) has a Borel exceptional value b∈(C\{0})∪{∞},it is proved that max{τ(f(z)),τ(△cf(z)/f(z))}=max{τ(△cf(z)/f(z)),τ(f(z+c))}=σ(f(z)) unless f(z) takes a special form.Here τ(g(z)) denotes the exponent of convergence of fixed points of the meromorphic function g(z),and σ(g(z)) denotes the order of growth of g(z). 相似文献
15.
Herbert E. Salzer 《Numerische Mathematik》1964,6(1):68-77
Divided differences forf (x, y) for completely irregular spacing of points (x i ,y i ) are developed here by a natural generalization of Newton's scheme. Existing bivariate schemes either iterate the one-dimensional scheme, thus constraining (x i ,y i ) to be at corners of rectangles, or give polynomials Σa jk x j y k having more coefficients than interpolation conditions. Here the generalizedn th divided difference is defined by (1)\(\left[ {01... n} \right] = \sum\limits_{i = 0}^n {A_i f\left( {x_i , y_i } \right)} \) where (2)\(\sum\limits_{i = 0}^n {A_i x_i^j , y_i^k = 0} \), and 1 for the last or (n+1)th equation, for every (j, k) wherej+k=0, 1, 2,... in the usual ascending order. The gen. div. diff. [01...n] is symmetric in (x i ,y i ), unchanged under translation, 0 forf (x, y) an, ascending binary polynomial as far asn terms, degree-lowering with respect to (X, Y) whenf(x, y) is any polynomialP(X+x, Y+y), and satisfies the 3-term recurrence relation (3) [01...n]=λ{[1...n]?[0...n?1]}, where (4) λ= |1...n|·|01...n?1|/|01...n|·|1...n?1|, the |...i...| denoting determinants inx i j y i k . The generalization of Newton's div. diff. formula is (5)
$$\begin{gathered} f\left( {x, y} \right) = f\left( {x_0 , y_0 } \right) - \frac{{\left| {\alpha 0} \right|}}{{\left| 0 \right|}}\left[ {01} \right] + \frac{{\left| {\alpha 01} \right|}}{{\left| {01} \right|}}\left[ {012} \right] - \frac{{\left| {\alpha 012} \right|}}{{\left| {012} \right|}}\left[ {0123} \right] + \cdots + \hfill \\ + \left( { - 1} \right)^n \frac{{\left| {\alpha 01 \ldots n - 1} \right|}}{{\left| {01 \ldots n - 1} \right|}}\left[ {01 \ldots n} \right] + \left( { - 1} \right)^{n + 1} \frac{{\left| {\alpha 01 \ldots n} \right|}}{{\left| {01 \ldots n} \right|}}\left[ {01 \ldots n} \right], \hfill \\ \end{gathered} $$ 相似文献
16.
S. V. Astashkin 《Functional Analysis and Its Applications》2008,42(2):144-147
Let X be a separable or maximal rearrangement invariant space on [0, 1]. Necessary and sufficient conditions are found under which the generalized Khintchine inequality holds for an arbitrary sequence {?k} k=1 ∞ ? X of mean zero independent variables. Moreover, the subspace spanned in a rearrangement invariant space by the Rademacher system with independent vector coefficients is studied.
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$\left\| {\sum\limits_{k = 1}^\infty {f_k } } \right\|_X \leqslant C\left\| {\left( {\sum\limits_{k = 1}^\infty {f_k^2 } } \right)^{1/2} } \right\|_X $
17.
Hrmander Type Theorem for Fourier Multipliers with Optimal Smoothness on Hardy Spaces of Arbitrary Number of Parameters 下载免费PDF全文
Jiao Chen 《数学学报(英文版)》2017,33(8):1083-1106
The main purpose of this paper is to establish the Hormander-Mihlin type theorem for Fourier multipliers with optimal smoothness on k-parameter Hardy spaces for k≥ 3 using the multiparameter Littlewood-Paley theory. For the sake of convenience and simplicity, we only consider the case k = 3, and the method works for all the cases k≥ 3:■where x =(x_1,x_2,x_3)∈R~(n_1)×R~(n_2)×R~(n_3) and ξ =(ξ_1,ξ_2,ξ_3)∈R~(n_1)×R~(n_2)×R~(n_3). One of our main results is the following:Assume that m(ξ) is a function on R~(n_1+n_2+n_3) satisfying ■ with s_i n_i(1/p-1/2) for 1≤i≤3. Then T_m is bounded from H~p(R~(n_1)×R~(n_2)×R~(n_3) to H~p(R~(n_1)×R~(n_2)×R~(n_3)for all 0 p≤1 and ■ Moreover, the smoothness assumption on s_i for 1≤i≤3 is optimal. Here we have used the notations m_(j,k,l)(ξ)=m(2~jξ_1,2~kξ_2,2~lξ_3)Ψ(ξ_1)Ψ(ξ_2)Ψ(ξ_3) and Ψ(ξ_i) is a suitable cut-off function on R~(n_i) for1≤i≤3, and W~(s_1,s_2,s_3) is a three-parameter Sobolev space on R~(n_1)×R~(n_2)× R~(n_3).Because the Fefferman criterion breaks down in three parameters or more, we consider the L~p boundedness of the Littlewood-Paley square function of T_mf to establish its boundedness on the multi-parameter Hardy spaces. 相似文献
18.
V. A. Yudin 《Proceedings of the Steklov Institute of Mathematics》2011,273(1):188-189
It is established that H. Bohr’s inequality \(\sum\nolimits_{k = 0}^\infty {\left| {{{f^{\left( k \right)} \left( 0 \right)} \mathord{\left/ {\vphantom {{f^{\left( k \right)} \left( 0 \right)} {\left( {2^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} k!} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} k!} \right)}}} \right| \leqslant \sqrt 2 \left\| f \right\|_\infty }\) is sharp on the class H ∞. 相似文献
19.
Rafael de la Llave 《Regular and Chaotic Dynamics》2017,22(6):650-676
We present simple proofs of a result of L.D. Pustylnikov extending to nonautonomous dynamics the Siegel theorem of linearization of analytic mappings. We show that if a sequence f n of analytic mappings of C d has a common fixed point f n (0) = 0, and the maps f n converge to a linear mapping A∞ so fast that then f n is nonautonomously conjugate to the linearization. That is, there exists a sequence h n of analytic mappings fixing the origin satisfying The key point of the result is that the functions hn are defined in a large domain and they are bounded. We show that We also provide results when f n converges to a nonlinearizable mapping f∞ or to a nonelliptic linear mapping. In the case that the mappings f n preserve a geometric structure (e. g., symplectic, volume, contact, Poisson, etc.), we show that the hn can be chosen so that they preserve the same geometric structure as the f n . We present five elementary proofs based on different methods and compare them. Notably, we consider the results in the light of scattering theory. We hope that including different methods can serve as an introduction to methods to study conjugacy equations.
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$$\sum\limits_n {{{\left\| {{f_m} - {A_\infty }} \right\|}_{L\infty \left( B \right)}} < \infty } $$
$${A_\infty } = diag\left( {{e^{2\pi i{\omega _1}}},...,{e^{2\pi i{\omega _d}}}} \right)\omega = \left( {{\omega _1},...,{\omega _q}} \right) \in {\mathbb{R}^d},$$
$${h_{n + 1}} \circ {f_n} = {A_\infty }{h_n}.$$
$${\sum\nolimits_n {\left\| {{h_n} - Id} \right\|} _{L\infty (B)}} < \infty .$$
20.
M. G. Grigoryan K. A. Navasardyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2016,51(1):21-33
The paper proves that for any ε > 0 there exists ameasurable set E ? [0, 1] with measure |E| > 1 ? ε such that for each f ∈ L1[0, 1] there is a function \(\tilde f \in {L^1}\left[ {0,1} \right]\) coinciding with f on E whose Fourier-Walsh series converges to \(\tilde f\) in L1[0, 1]-norm, and the sequence \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \) is monotonically decreasing, where \(\left\{ {{c_k}\left( {\tilde f} \right)} \right\}\) is the sequence of Fourier-Walsh coefficients of \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \). 相似文献