共查询到20条相似文献,搜索用时 15 毫秒
1.
Oktay A. Veliev 《Central European Journal of Mathematics》2011,9(3):657-672
We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential
equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas,
we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions
of the operator under consideration forms a Riesz basis. 相似文献
2.
A. I. Vagabov 《Differential Equations》2012,48(8):1051-1064
We consider a general pencil of linear ordinary differential operators under the weakest possible restrictions on the smoothness of the coefficients. A detailed analysis of the notion of regular boundary conditions is presented. An n-fold expansion formula is obtained. 相似文献
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A.G Ramm 《Journal of Mathematical Analysis and Applications》1981,80(1):57-66
When does the root system of a nonselfadjoint operator form a Riesz basis of a Hilbert space? This question is discussed in the paper. 相似文献
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Gerald Teschl 《Proceedings of the American Mathematical Society》2008,136(7):2473-2476
We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm-Liouville and Dirac operators by the eigenvalues of regular operators.
10.
Buchin Su 《Annali di Matematica Pura ed Applicata》1940,19(1):289-313
Sunto. The paper deals with many projective properties of the neighbourhoods of the third,4th, 5th order of a point on a non-holonome surfaceV
3
2
inS
3. Chiefly two remarkable projective correspondences are studied, between the tangent plane and the bundle of directions, with
his contact point as centre. Many generalizations are obtained of geometrical loci (so as lines, planes, quadrics) projectively
associated with the neighbourhoods of a point on an ordinary (holonome) surface. The last sections are concerned with the
extension to theV
3
2
of the quadric ofMoutard and theSegre's correspondence.
相似文献
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Albrecht Böttcher Harold Widom 《Journal of Mathematical Analysis and Applications》2006,322(2):990-1000
We consider the operator of taking the 2pth derivative of a function with zero boundary conditions for the function and its first p−1 derivatives at two distinct points. Our main result provides an asymptotic formula for the eigenvalues and resolves a question on the appearance of certain regular numbers in the eigenvalue sequences for p=1 and p=3. 相似文献
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Support by DFG contract Ja 511/1-1 is gratefully acknowledged 相似文献
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V. M. Kurbanov 《Differential Equations》2013,49(4):437-449
We consider an ordinary differential operator of arbitrary order, obtain necessary conditions for the Riesz property of systems of normalized root functions, prove an analog of the Riesz theorem, and use it to obtain sufficient conditions for the basis property of the system of root functions of the given operator in L p . 相似文献
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A. A. Shkalikov 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):284-298
We study perturbations of a self-adjoint operator T with discrete spectrum such that the number of its points on any unit-length interval of the real axis is uniformly bounded.
We prove that if ‖Bϕ
n
‖ ≤ const, where ϕ
n
is an orthonormal system of eigenvectors of the operator T, then the system of root vectors of the perturbed operator T + B forms a basis with parentheses. We also prove that the eigenvalue-counting functions of T and T + B satisfy the relation |n(r, T) − n(r, T + B)| ≤ const. 相似文献
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A. S. Tsareva 《Differential Equations》2008,44(3):364-373
On a finite interval G of the real line, we consider the root functions of an ordinary second-order differential operator without any boundary conditions for the case in which the imaginary part of the spectral parameter is unbounded.We refine the estimates for the C-and L p -norms of a root function and its first derivative on a compact set contained in the interior of G for the case in which the Carleman condition fails.A sufficient condition is obtained for the root functions of an ordinary second-order differential operator to have the Bessel property, assuming that the Carleman condition fails. We show that, under certain conditions, this problem can be reduced to analyzing the Bessel property of systems of exponentials. 相似文献