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 Mat. Zametki, 1997, Volume 62, Issue 3, Pages 418–424 (Mi mz1623)

A first-order boundary value problem with boundary condition on a countable set of points

A. M. Minkin

Saratov State University named after N. G. Chernyshevsky

Abstract: Let $E=\{E_n\}$ be the family of subspaces spanning the eigenfunctions and adjoint functions of the boundary-value problem
$$-i\frac{dy}{dx}=\lambda y,\quad -a\le x\le a,\qquad U(y)\equiv\int_{-a}^ay(t)d\sigma(t)=0,$$
that correspond to “close” eigenvalues (in the sense of the distance defined as the maximal of the Euclidean and the hyperbolic metrics). For a purely discrete measure $d\sigma$ it is shown that the system $E$ does not form an unconditional basis of subspaces in $L^2(-a,a)$ if at least one of the end points $\pm a$ is mass-free.

DOI: https://doi.org/10.4213/mzm1623

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English version:
Mathematical Notes, 1997, 62:3, 350–355

Bibliographic databases:

UDC: 517.512.5
Revised: 05.12.1996

Citation: A. M. Minkin, “A first-order boundary value problem with boundary condition on a countable set of points”, Mat. Zametki, 62:3 (1997), 418–424; Math. Notes, 62:3 (1997), 350–355

Citation in format AMSBIB
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