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81.
A. J. Mkrtchyan 《Mathematische Nachrichten》2019,292(11):2441-2451
For multiple power series centered at the origin we consider the problem of its analytic continuability into a sectorial domain. The condition for continuability is formulated in terms of a holomorphic function that interpolates the series coefficients. For series in one variable this problem has been studied in the works of E. Lindelöf, N. Arakelian, and others. 相似文献
82.
In this note, we prove the boundary unique continuation property for harmonic function dfined on convex domain 相似文献
83.
Michele Di Cristo Luca Rondi Sergio Vessella 《Annali di Matematica Pura ed Applicata》2006,185(2):223-255
We treat the stability issue for an inverse problem arising from non-destructive evaluation by thermal imaging. We consider
the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a
parabolic initial-boundary value problem. We obtain that when the unknown part of the boundary is a priori known to be smooth,
the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed.
Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions
on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given
the exponential ill-posedness, the stability estimate obtained is optimal.
AMS 2000 Mathematics Subject Classification. Primary 35R30, Secondary 35B60, 33C90 相似文献
84.
We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L2 space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an “unwrapped” version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities. 相似文献
85.
On unique range sets for meromorphic or entire functions 总被引:5,自引:0,他引:5
This paper has studied the Gross uniqueness question ignoring multiplicity and relating multiple values, and extended and
improved on some related results in [1–8].
Supported in part by National Natural Science Foundation of China 相似文献
86.
设w(r)非负非增δ〉0,D为平面上的区域,Z0∈αD,u是D上的一个二阶椭圆方程的解,且│u(z)│≤Cexp(-w(│z-z0│)(A)我们证明了,如果∫^δ0w(r)dr=∞,则u=0,若∫^δ0w(r)dr〈∞,则有上半平面上的有界调和函数u使(A)成立。 相似文献
87.
Lord–;Shulman's system of partial differential equations of generalized thermoelasticity [1] is considered, in which the finite velocity of heat propagation is taken into account by introducing a relaxation time constant. General aspects of the theory of boundary value and initial-boundary value problems and representation of solutions by series and quadratures are considered using the method of a potential. 相似文献
88.
S. Saks and recently R.D. Mauldin asked if every translation invariant σ-finite Borel measure on Rd is a constant multiple of Lebesgue measure. The aim of this paper is to investigate the versions of this question, since surprisingly the answer is “yes and no,” depending on what we mean by Borel measure and by constant. According to a folklore result, if the measure is only defined for Borel sets, then the answer is affirmative. We show that if the measure is defined on a σ-algebra containing the Borel sets, then the answer is negative. However, if we allow the multiplicative constant to be infinity, then the answer is affirmative in this case as well. Moreover, our construction also shows that an isometry invariant σ-finite Borel measure (in the wider sense) on Rd can be non-σ-finite when we restrict it to the Borel sets. 相似文献
89.
The Euclidean distance matrix (EDM) completion problem and the positive semidefinite (PSD) matrix completion problem are considered in this paper. Approaches to determine the location of a point in a linear manifold are studied, which are based on a referential coordinate set and a distance vector whose components indicate the distances from the point to other points in the set. For a given referential coordinate set and a corresponding distance vector, sufficient and necessary conditions are presented for the existence of such a point that the distance vector can be realized. The location of the point (if it exists) given by the approaches in a linear manifold is independent of the coordinate system, and is only related to the referential coordinate set and the corresponding distance vector. An interesting phenomenon about the complexity of the EDM completion problem is described. Some properties about the uniqueness and the rigidity of the conformation for solutions to the EDM and PSD completion problems are presented. 相似文献
90.
M. A. Oliver 《Foundations of Physics Letters》1991,4(4):337-350
The distribution of astronomical redshifts and the cosmic background radiation define a unique inertial reference frame. This paper contains an investigation of questions concerning quantum theory which arise with the introduction of a unique rest frame into spacetime. The Mössbauer effect, photon pair production, and photoelectric effect are treated together with photon scattering by a moving reflector and the Compton effect. Dirac's 1928 quantum theory of electrons is shown to yield its well-known energy spectrum for the hydrogen atom independently of the velocity of the atom relative to the rest frame.1. Address for the academic year 1990–91: 415 Graduate Studies Research Center, University of Georgia, Athens, Georgia 30602, USA. 相似文献