共查询到20条相似文献,搜索用时 15 毫秒
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Dirac operator with eigenvalue-dependent boundary and jump conditions is studied. Uniqueness theorems of the inverse problems from either Weyl function or the spectral data (the sets of eigenvalues and norming constants except for one eigenvalue and corresponding norming constant; two sets of different eigenvalues except for two eigenvalues) are proved. Finally, we investigate two applications of these theorems and obtain analogues of a theorem of Hochstadt-Lieberman and a theorem of Mochizuki-Trooshin. 相似文献
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In this paper, Dirac operator with some integral type nonlocal boundary conditions is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we give an algorithm for the reconstruction of some coefficients of the operator. 相似文献
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We deal with the Dirac operator with eigenvalue dependent boundary and jump conditions. Properties of eigenvalues, eigenfunctions
and the resolvent operator are studied. Moreover, uniqueness theorems of the inverse problem according to the Weyl functions
and the spectral data (the sets of eigenvalues and norming constants; two different eigenvalues sets) are proved. 相似文献
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José-Luis Menaldi 《Journal of Differential Equations》2007,237(1):77-115
We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-differential operator with Wentzell boundary conditions. 相似文献
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Tatiana V. Savina 《Journal of Mathematical Analysis and Applications》2010,370(2):716-1163
The biharmonic equation arises in areas of continuum mechanics including linear elasticity theory and the Stokes flows, as well as in a radar imaging problem. We discuss the reflection formulas for the biharmonic functions u(x,y)∈R2 subject to different boundary conditions on a real-analytic curve in the plane. The obtained formulas, generalizing the celebrated Schwarz symmetry principle for harmonic functions, have different structures. In particular, in the special case of the boundary, Γ0:={y=0}, reflections are point-to-point when the given on Γ0 conditions are u=n∂u=0, u=Δu=0 or n∂u=n∂Δu=0, and point to a continuous set when u=n∂Δu=0 or n∂u=Δu=0 on Γ0. 相似文献
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We consider the one-dimensional Dirac operator. We derive a shift formula for its root vector functions and prove anti-a priori and two-sided estimates for various L p -norms of these functions. 相似文献
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A. M. Akhtyamov 《Differential Equations》2017,53(11):1515-1518
We describe all degenerate two-point boundary conditions possible in a homogeneous spectral problem for the diffusion operator. We show that the case in which the characteristic determinant is identically zero is impossible for the nonsymmetric diffusion operator and that the only possible degenerate boundary conditions are the Cauchy conditions. For the symmetric diffusion operator, the characteristic determinant is zero if and only if the boundary conditions are falsely periodic boundary conditions; the characteristic determinant is identically a nonzero constant if and only if the boundary conditions are generalized Cauchy conditions. 相似文献
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Fangbing Wu 《K-Theory》1993,7(2):145-174
A cyclic cocycle is constructed for the Dirac operator on a compact spin manifold with boundary with the -invariant cochain introduced as the boundary correction term. This cocycle is seen to satisfy certain growth condition weaker than being entire and its pairing with the Chern characters of idempotents as well as the relevant index formulae are studied. The -cochain is a generalization of the Atiyah-Patodi-Singer -invariant and it carries information on the APS -invariants for Dirac operators twisted by bundles. It is also shown that one obtains the transgressed Chern character, defined by Connes and Moscovici, by applying the boundary operatorB in the cyclic bicomplex to the higher components of the -cochain. 相似文献
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We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green function of the operator is given. 相似文献
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A. I. Ismailova 《Differential Equations》2012,48(2):296-300
We consider the one-dimensional Dirac operator on an arbitrary interval and obtain a mean value formula for the root vector
functions of this operator. 相似文献
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We develop variational formulas for certain Neumann and Green functions of multiply connected planar domains, valid for any
smooth homotopy of the boundary. The modified Neumann and Green functions under consideration arise in the study of holomorphic
functions with single-valued primitives. 相似文献
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We establish a criterion for the Riesz property of systems of root vector functions of the one-dimensional Dirac operator. 相似文献
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A spectral problem for the one-dimensional Dirac system is considered. The question of the number of zeros for the components of the eigenvector functions of this problem is studied. 相似文献
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Given the spectrum of the Dirac operator, together with the potential on the half-interval and one boundary condition, this paper provides reconstruction of the potential on the whole interval, and proves the existence conditions of the solution. 相似文献
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The main result of this paper is a generalization of the Mittag-Leffler theorem to matrix and operator valued meromorphic functions. Namely, a meromorphic matrix or operator valued function is constructed when the singular parts of the function and if its inverse are given in all singular points (which are assumed to be isolated). The paper contains also interpolation theorems based on other forms of local data (Jordan chains from left and right of the function and its inverse). An analysis of the local data, which is used in the proofs of these theorems is also included.Dedicated to the memory of D.P. MilmanThe research of this author partially supported by the Fund for Basic Research administrated by the Israel Academy of Science and Humanities. 相似文献