Functional Model of Dissipative Fourth Order Differential Operators

Abstract

In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which based on the method of Pavlov and define its characteristic function. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative fourth order operators.

On extensions of singular fourth order dynamic operators on time scales

“…Using this notion, they described all maximal dissipative, accretive, self-adjoint extensions of symmetric operators. This problem has been investigated by many mathematicians (see [5], [6], [8]- [17]). For a more comprehensive discussion of extension theory of symmetric operators, the reader is referred to [3].…”

Transverse vibration of nonuniform Euler-Bernoulli beams on bounded Time scales

“…They described all maximal dissipative, accretive, self adjoint extensions of symmetric operators. This problem has been investigated by many mathematicians (see [13]- [20]). For a more comprehensive discussion of extension theory of symmetric operators, the reader is referred to [26].…”

Dissipative Sturm-Liouville Operators with Transmission Conditions

“…Spectral theory is one of the main branches of modern functional analysis and it has many applications in mathematics and applied sciences. There has recently been great interest in spectral analysis of Sturm-Liouville boundary value problems with eigenparameter-dependent boundary conditions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). Furthermore, many researchers have studied some boundary value problems that may have discontinuities in the solution or its derivative at an interior point [15][16][17][18][19].…”