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Various BMO-type characteristics are given for some class of holomorphic functions with a mixed norm. Some criteria are established for Blaschke products to belong to analytic Besov spaces.  相似文献   

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We introduce a new parametric representation of the class of holomorphic functions in the unit disk such that their Nevanlinna characteristic has a power growth near the boundary of the disk. The parameters of the obtained representation are determined explicitly by values of the function. In addition, the set of multipliers from the considered class to the Hardy and Bergman classes and the disk algebra is described completely. Bibliography: 10 titles.  相似文献   

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We suggest an explicit formula for reconstruction of a harmonic function in a domain from its values and the values of its normal derivative on part of the boundary; i.e., we give an explicit continuation formula and a regularization procedure for a solution to the Cauchy problem for the Laplace equation.  相似文献   

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We consider the Cauchy problem for the Helmholtz equation in an arbitrary bounded planar domain with Cauchy data only on part of the boundary of the domain. We derive a Carleman-type formula for a solution to this problem and give a conditional stability estimate.  相似文献   

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The authors prove Carleman estimates for the Schr(o)dinger equation in Sobolev spaces of negative orders,and use these estimates to prove the uniqueness in the inverse problem of determining Lp-potentials.An L2-1evel observability inequality and unique continuation results for the Schr(o)dinger equation are also obtained.  相似文献   

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Let Δ be an equilateral cone in C with vertices at the complex numbers and rigid base M (Section 1). Assume that the positive real semi-axis is the bisectrix of the angle at the origin. For the base M of the cone Δ we derive a Carleman formula representing all those holomorphic functions from their boundary values (if they exist) on M which belong to the class . The class is the class of holomorphic functions in Δ which belong to the Hardy class near the base M (Section 2). As an application of the above characterization, an important result is an extension theorem for a function fL1(M) to a function .  相似文献   

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We give necessary and sufficient conditions for totally real sets in Stein manifolds to admit Carleman approximation of class Ck{mathcal C^k}, k ≥ 1, by entire functions.  相似文献   

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This paper presents a definition of residue formulas for the Euler class of cohomology-oriented sphere fibrations ξ. If the base of ξ is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].  相似文献   

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The unique continuation theorems for the anisotropic partial differential-operator equations with variable coeffcients in Banach-valued Lp-spaces are studied.To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations,the suffcient conditions are founded.By using these facts,the unique continuation properties are established.In the application part,the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.  相似文献   

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For infinitely multiple exponentials with two alternating exponents, we construct continuations to unbounded domains, so that these continuations are the limit functions of sequences of finitely multiple exponentials. We prove that, for different exponents, such a continuation is unique in the class of continuously differentiable functions. We extend the domain of existence of infinitely multiple exponentials. For exponents with the same signs, this domain remains bounded, while for exponents with different signs, it coincides with the number axis.  相似文献   

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汪和平 《数学进展》1997,26(2):123-128
考虑对具有有界混合差分的二元光滑函数类B^γ,p,θ的求积公式,本文证明了Fibonacci求积公式是渐近最优的,并求出了春误差的渐近最优价。  相似文献   

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This work is a survey of results for ill-posed Cauchy problems for PDEs of the author with co-authors starting from 1991. A universal method of the regularization of these problems is presented here. Even though the idea of this method was previously discussed for specific problems, a universal approach of this paper was not discussed, at least in detail. This approach consists in constructing of such Tikhonov functionals which are generated by unbounded linear operators of those PDEs. The approach is quite general one, since it is applicable to all PDE operators for which Carleman estimates are valid. Three main types of operators of the second order are among them: elliptic, parabolic and hyperbolic ones. The key idea is that convergence rates of minimizers are established using Carleman estimates. Generalizations to nonlinear inverse problems, such as problems of reconstructions of obstacles and coefficient inverse problems are also feasible.  相似文献   

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引进并研究用Ruscheweyh导数定义的解析函数类Sk,[λα,β,ρ].结合算子理论导出类中函数的积分表达式、偏差定理,讨论类中函数的半径问题和Hadamard卷积性质.  相似文献   

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In this paper, we prove Brennan's conjecture for conformal mappings f of the disk {z : | z| < 1} assuming that the Taylor coefficients of the function log(zf′(z)/f(z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle |z| = r of the squared modulus of the function zf′(z)/f(z).  相似文献   

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