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

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


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


differential operator, block-triangular operator potential, Par- seval equality.


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

pp. (Russian). (English transl.: (1963). Gordon and Breach Science Publishers, New York-London,

xiii+291 pp.)

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

electronic systems, 5, (2000), no. 3, 6 { 24 (Russian) (English. Transl.: Telecommun. And Radio Eng. 56

(2001), (no. 8 and 9), 4 { 29).

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

efficients, J. of Basic and Applied Research International, 16 (2016), (no. 2), 116 { 121.

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

tential, Abstract and Applied Analysis, 2016 (2016), 1 { 6.

A.M. Kholkin, The Series Expansion of the Greens Function of a Differential Operator with Block-

Triangular Operator Potential, British J. of Mathematics & ComputerScience; 19 (2016); (no: 5); 1 􀀀 12:

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 (2015), (no. 5),

{ 775.

A. M. Kholkin and F. S. Rofe-Beketov, Sturm type oscillation theorems for equations with block-triangular

matrix coefficients, Methods of Functional Analysis and Topology, 18 (2012), (no. 2), 176 { 188.

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

with operator-valued coefficients, Azerbaijan Journal of Mathematics, 3 (2013), (no. 2), 3 { 44.

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

coefficients, Journal Math. Physics, Analysis, Geometry, 10 (2014), (no. 1), 44 { 63.

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

Nauk SSSR, 154 (1964), (no. 5), 1030 { 1033.

V. A. Marchenko, Spectral Theory of Sturm-Liouville Operastors, Naukova Dumka, Kiev, 1972 (Russian).

V. A. Marchenko, Sturm-Liouville operators and their applications, 331 pp., Naukova Dumka, Kiev, 1977,

(Russian) (English Transl: Oper. Theory Adv. Appl. 22 (1986), Birkhauser Verlag, Basel, xii+367pp.;

revised edition AMS Chelsea Publishing, Providence R.I., 2011, xiv+396 pp.).

M. A. Naimark, Linear differential operators, 526 pp., Nauka, Moscow,, 1969, (Russian) (English Transl:

Part I: Frederick Ungar Publishing Co., New York, 1968; Part II: With additional material by the author,

and a supplement by V.E. Lyantse, English translation edited by W.N. Everitt Frederick Ungar Publishing

Co., New York, 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 (1954), 181 { 270.

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 (1960), (no. 3), 293 { 342.

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 (2011), (no. 2), 3 { 69.

J. T. Schwartz, Some nonselfadjoint operators, Comm. for pure and appl. Math., XIII (1960), 609 { 639.


  • There are currently no refbacks.

free counters