eigenfunctions

The Principle of Localization at the Class of Functions Integrable in the Riemann for the Processes of Lagrange –Sturm – Liouville

Authors: Trynin A. Y., Kireeva E. D.

Let us say that the principle of localization holds at the class of functions F at point x0 ∈ [0, π] for the Lagrange –Sturm – Liouville interpolation process L SL n (f, x) if limn→∞ L SL n (f, x0) − L SL n (g, x0) = 0 follows from the fact that the condition f(x) = g(x) is met for any two functions f and g belonging to F in some neighborhood Oδ(x0), δ > 0.

Equiconvergence Theorem for Integral Operator with Involution

Authors: Nazarova E. V., Khalova V. A.

In the paper, the integral operator with kernel having discontinuities of the first kind at the lines t = x and t = 1 − x is studied. The equiconvergence of Fourier expansions for arbitrary integrable function f(x) in eigenfunctions and associated functions of the considered operator and expansions of linear combination of functions f(x) and f(1 − x) in trigonometric system is proved. The equiconvergence is studied using the method based on integration of the resolvent using spectral value. Methods, developed by A. P.

On Riesz Basises of Eigenfunctions of Integral Operators with Kernels Discontinuous on Broken Lines

Authors: Kurdyumov V. P.

For the integral operator, which kernel has jump discontinuities on the sides and diagonals of the four equal subsquares of the unit square 0 ≤ x, t ≤ 1, Riesz basisness of its eigen and associated functions is proved.

Dynamics of Multilayered Thermoviscoelastic Plates

Authors: Kovalev V. A.

This paper deal with laminated thin-walled structures. The laminated structures considered herein consist of three layers. The following assumptions are assumed. The thickness of inner layer is considerably greater the others.The kine matic relationsf ortheinnerlayerare examined in the form of Mindlin – Reissner shell theory, for the outer layers are in the form of membrane theory. The deformations of the whole layered structure are defined by the polyline hypothesis.

On Propertiesofthe Eigenfunctionsofa Quadratic Pencilofthe Second Order Differential Operators

Authors: Rykhlov V. S.

The degenerated second order ordinary differential quadratic pencil with constant coefficients is considered. The case is studied, when the roots of characteristic equation lie on a straight line coming through the origin and on the both side of the origin. Properties of the system of its eigenfunctions in the spaces L2[0,σ], σ > 0 is investigated. Criteria of one-fold completeness and minimality of this systemareprovedandsufficientconditionsofone-foldcompleteness and minimality are found.