Solvability of an Unbounded Operator Equation
DOI:
https://doi.org/10.29304/jqcsm.2024.16.21553Keywords:
Operator Equations, Semigroup, Unbounded Operator, Generalized SemigroupAbstract
In this work, we will submit the form of the solution of the generalization kind of unbounded operator equation define on Hilbert space which is , where is the bounded operator satisfy the above operator equations and showing this solution via application the semigroup theory, moreover we will discuss some properties of this solution and proved its unique. Also, it was proved that for a locally bounded operator satisfying the equation.
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V. S. Belonosov, “INSTABILITY INDICES OF DIFFERENTIAL OPERATORS,” Mathematics of the USSR-Sbornik, vol. 57, no. 2, pp. 507–525, Feb. 1987, doi: 10.1070/SM1987v057n02ABEH003083.
T. Nambu, “Feedback stabilization of diffusion equations by a functional observer,” J Differ Equ, vol. 43, no. 2, pp. 257–280, Feb. 1982, doi: 10.1016/0022-0396(82)90094-8.
M. Rosenblum, “The Operator Equation BX - XA = Q with Selfadjoint A and B,” Proceedings of the American Mathematical Society, vol. 20, no. 1, p. 115, Jan. 1969, doi: 10.2307/2035971.
V. Q. Phóng, “The operator equation AX - XB = C with unbounded operators A and B and related abstract Cauchy problems.,” Mathematische Zeitschrift, vol. 208, no. 4, pp. 567–588, 1991, [Online]. Available: http://eudml.org/doc/174337
S. Schweiker, “Mild solutions of second-order differential equations on the line,” in Mathematical Proceedings of the Cambridge Philosophical Society, 2000, vol. 129, no. 1, pp. 129–151. doi: 10.1017/S0305004199004351.
N. T. Lan, “ On the operator equation A X−X B=C with unbounded operators A,B , and C ,” in Abstract and Applied Analysis, 2001, vol. 6, no. 6, pp. 317–328. doi: 10.1155/s1085337501000665.
N. A. Caruso and A. Michelangeli, “Krylov Solvability of Unbounded Inverse Linear Problems,” Integral Equations and Operator Theory, vol. 93, no. 1, p. 1, Feb. 2021, doi: 10.1007/s00020-020-02616-2.
E. Kreyszig, Introductory functional analysis with applications, vol. 17. John Wiley & Sons, 1991.
A. Pazy, Semigroups of linear operators and applications to partial differential equations, vol. 44. Springer Science & Business Media, 2012.
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Copyright (c) 2024 Karrar Mohammed Kadhim
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