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1.
For a nonempty setE of nonnegative integers letH
E
p, q, a
andH
E
p
be the closed linear span of
相似文献
2.
《复变函数与椭圆型方程》2012,57(10):881-889
In the present paper we have deduced the necessary and sufficient conditions on which an initial value problem $\fraca {\partial w}{\partial z_j} = a_j(z,\overline {z})\overline {w}+b_j(z,\overline {z})w+c_j(z,\overline {z}), \, j = 1,\ldots , n,\, w(z_0,\overline {z_0}) = w_0$ is locally solvable in the class of generalized analytic functions of several complex variables, which are functions fulfilling generalized Cauchy-Riemann System, $\fraca {\partial w}{\partial \overline {z_k}} = \overline {\alpha _k(z,\overline {z})}\, \overline {w}+ \overline {\beta _k(z,\overline {z})}w+ \overline {\gamma _k(z,\overline {z})},\, k = 1,\ldots , n$ . 相似文献
3.
A sufficient condition is obtained for the minimality of the complex exponential system E(A, M) = {z^le^λnz: l = 0, 1,,.., mn - 1; n = 1, 2,...} in the Banaeh space La^p consisting of all functions f such that f^-a ∈ LP(N). Moreover, if the incompleteness holds, each function in the closure of the linear span of exponential system E(A, M) can be extended to an analytic function represented by a Taylor-Dirichlet series. 相似文献
4.
In this paper, we consider a general nonlinear integral operator H_(αi),β_i(f_1,..., f_n;g_1,..., g_n)(z). Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between H_(αi),β_i(f_1,..., f_n; g_1,..., g_n)(z) and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results. 相似文献
5.
For positive integers with a
r
= 2, the multiple zeta value or r-fold Euler sum is defined as [2]
6.
The Ramanujan Journal - Let $$(m_1,\ldots ,m_J)$$ and $$(r_1,\ldots ,r_J)$$ be two sequences of J positive integers satisfying $$1\le r_j< m_j$$ for all $$j=1,\ldots ,J$$ . Let $$(\delta... 相似文献
7.
《复变函数与椭圆型方程》2012,57(2):149-154
Let G be the algebraic limit of a sequence $ \{ G_m\} $ of r generator subgroups of $ M(\bar {R}^n) $ . We prove that (i) if $ G_m $ is elementary, then G is elementary; (ii) if $ G_m $ is not non-elementary and non-discrete and G satisfies the Condition A, then G is not non-elementary and non-discrete. Let $ E_l = \{ (f_1, f_2,\ldots ,f_l): f_1,f_2,\ldots ,f_l\in M(\bar {R}^2), \langle \,f_1,f_2,\ldots , \,f_l \rangle\ elementary\} $ and $ D_l = \{ (f_1,f_2,\ldots ,f_l): f_1,f_2,\ldots ,f_l\in M(\bar {R}^2), \langle \,f_1,f_2,\ldots ,f_l \rangle\ discrete\} $ . we obtain that the set $ E_l , D_l\cup E_l $ and $ D_l\cap E_l^c $ are closed in $ \underbrace {M(\bar {R}^2)\times \cdots \times M(\bar {R}^2)}\limits _{l} $ . 相似文献
8.
The embedding of the anisotropic spaces $B_{p_1 , \ldots ,p_n ,\theta }^{\omega _1 , \ldots ,\omega _n } \left( {\mathbb{R}^n } \right)$ with mixed norm is studied. We establish some necessary and sufficient conditions of the embedding $B_{p_1 , \ldots ,p_n ,\theta }^{\omega _1 , \ldots ,\omega _n } \left( {\mathbb{R}^n } \right) \subset L^{q_1 , \ldots ,q_n } \left( {\mathbb{R}^n } \right)$ . 相似文献
9.
We present new algorithms for computing the values of the Schur and Jack functions in floating point arithmetic. These algorithms deliver guaranteed high relative accuracy for positive data ( 0$">) and run in time that is only linear in .
10.
Acta Mathematica Hungarica - Alon [1] proved that if $$p$$ is an odd prime, $$1\le n < p$$ and $$a_1,\ldots,a_n$$ are distinct elements in $$Z_p$$ and $$b_1,\ldots,b_n$$ are arbitrary... 相似文献
11.
Let \(x_{n,k}^{(\alpha ,\beta )}\) , \(k=1,\ldots ,n\) , be the zeros of Jacobi polynomials \(P_{n}^{(\alpha ,\beta )}(x)\) arranged in decreasing order on \((-1,1)\) , where \(\alpha ,\beta >-1\) , and \(\theta _{n,k}^{(\alpha ,\beta )}=\arccos x_{n,k}^{(\alpha ,\beta )}\) . Gautschi, in a series of recent papers, conjectured that the inequalities $$n\theta_{n,k}^{(\alpha,\beta)}<(n+1)\theta_{n+1,k}^{(\alpha,\beta)} $$ and $$(n+(\alpha+\beta+3)/2)\theta_{n+1,k}^{(\alpha,\beta)}<(n+(\alpha+\beta+1)/2)\theta_{n,k}^{(\alpha,\beta)}, $$ hold for all \(n\geq 1\) , \(k=1,\ldots ,n\) , and certain values of the parameters \(\alpha \) and \(\beta \) . We establish these conjectures for large domains of the \((\alpha ,\beta )\) -plane by using a Sturmian approach. 相似文献
12.
In this paper, we are concerned with the existence criteria for positive solutions of the following nonlinear arbitrary order
fractional differential equations with deviating argument
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