Parseval Equality for Non-Self-Adjoint Differential Op- erator with Block-Triangular Potential

A. M. Kholkin, F. S. Rofe-Beketov


Parseval equality is proved for Sturm-Liouville equation with block-triangular, increasing at innity operator potential.


differential operator, block-triangular operator potential, Parseval equality

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A. M. Kholkin and F. S. Rofe-Beketov, Sturm type oscillation theorems for equa-

tions with block-triangular matrix coefficients, Methods of Functional Analysis and

Topology, 18 (2): 176 { 188, 2012.

A. M. Kholkin and F. S. Rofe-Beketov, Sturm type theorems for differential equations

of arbitrary order with operator-valued coefficients, Azerbaijan Journal of Mathemat-

ics, 3 (2): 3 { 44, 2013.

M. A. Naimark, Linear differential operators, M.: Nauka, 1969, (Russian) (English

Transl: Part I: New York: Frederick Ungar Publishing Co., 1968; Part II: With addi-

tional material by the author, and a supplement by V.E. Lyantse, English translation

edited by W.N. Everitt, New York: Frederick Ungar Publishing Co., 1969).

M. A. Naimark, Investigation of the spectrum and the expansion in eigenfunctions of

a second-order non-self-adjoint differential operator on a semi-axis, Tr. Mosk. Mat.

Obs., 3 : 181 { 270, 1954.

V.E. Lyantse, On non-self-adjoint second-order differential operators on the semi-

axis, Doklady Akademii Nauk SSSR, 154 (5): 1030 { 1033, 1964.

V. A. Marchenko, Spectral Theory of Sturm-Liouville Operastors, Kiev: Naukova

Dumka, 1972, Russian.

V. A. Marchenko, Sturm-Liouville operators and their applications, Kiev: Naukova

Dumka, 1977, Russian (English Transl: Oper. Theory Adv. Appl. 22 , Basel:

Birkhauser Verlag, 1986; revised edition AMS Chelsea Publishing, Providence R.I.,


F.S. Rofe-Beketov, Expansion in eigenfunctions of innite systems of differential

equations in the non-self-adjoint and self- adjoint cases, Mat. Sb., 51 (3): 293 { 342,

J. T. Schwartz, Some nonselfadjoint operators, Comm. for pure and appl. Math.,

XIII: 609 { 639, 1960.

E. I. Bondarenko and F. S. Rofe-Beketov, Phase equivalent matrix potential, Elec-

tromagnetic waves and electronic systems, 5 (3): 6 { 24, 2000 Russian (English.

Transl.: Telecommun. And Radio Eng., 56 (8 and 9): 4 { 29, 2001).

F. S. Rofe-Beketov and E. I. Zubkova , Inverse scattering problem on the axis for

the triangular matrix potential a system with or without a virtual level , Azerbaijan

J. of Math., 1 (2): 3 { 69, 2011.

A. M. Kholkin and F. S. Rofe-Beketov, On spectrum of differential operators with

block - triangular matrix coefficients, Journal Math. Physics, Analysis, Geometry, 10

(1): 44 { 63, 2014.

A.M. Kholkin, Greens function for non-self-adjoint differential operator with block-

triangular operator coefficients, J. of Basic and Applied Research International, 16

(2): 116 { 121, 2016.

A. M. Kholkin, Resolvent for Non-self-Adjoint Differential Operator with Block-

Triangular Operator Potential, Abstract and Applied Analysis, 2016: 1 { 6, 2016.

A.M. Kholkin, The Series Expansion of the Greens Function of a Differential Oper-

ator with Block-Triangular Operator Potential, British J. of Mathematics And Com-

puter Science, 19 (5): 1 { 12, 2016.

A.M. Kholkin, Construction of the fundamental system of solutions for an operator

differential equation with a rapidly increasing at innity block triangular potential ,

Mathematica Aeterna, 5(5): 769 { 775, 2015.

Z. S. Agranovich and V. A. Marchenko, The inverse problem of scattering theory,

Kharkov: State Univ., 1960, Russian (English transl.: New York-London: Gordon

and Breach Science Publishers,1963).


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