On stability of closedness and self-adjointness for 2 × 2 operator matrices

Mathematical Notes - Consider an operator which is defined in Banach or Hilbert space X = X 1 × X 2 by the matrix $L = \left( {\begin{array}{*{20}{c}}A&;amp;B \\ C&;amp;D \end{array}}...     

Sturm-liouville operators with singular potentials

This paper deals with Sturm-Liouville operators generated on a finite interval and on the whole axis by the differential expressionl(y)=−y ^" +q(x)y, whereq(x) is a distribution of first order, such that . The minimal and maximal operators corresponding to potentials of this type on a finite interval are constructed. All self-adjoint extensions of the minimal operator are described and the asymptotics of the eigenvalues of these extensions is found. It is proved that the constructed operator coincides with the norm resolvent limit of the Sturm-Liouville operators generated by smooth potentialsq _n , provided that the condition holds. The convergence of the spectra of these operators to the spectrum of the limit operator is also proved. Similar results are obtained in the case of the whole axis. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 897–912, December, 1999.     

Ultrasonic stimulation of the migration of electron excitation energy via the phonon field

Following earlier papers reporting experimental establishment of cross-relaxation via the phonon field in the rf range, this paper theoretically demonstrates how energy migration via the phonon field in the optical range can be increased to experimentally detectable values.     

Differential Equations in Hilbert Space with Dissipative Symbols

In this article equations of the form