Equations in a Hilbert space whose solution sets are invariant with respect to a group isomorphic to a one-parameter group of unitary operators

Authors

  • V. Yu. Slyusarchuk Nat. Univ. farms and nature management, Rivne

Keywords:

Hilbert space, group of unitary operators

Abstract

We construct classes of equations in a Hilbert space whose sets of solution are invariant with respect to a group isomorphic to a one-parameter group of unitary operators. It is shown that the unbounded solutions of these equations are unstable.
The applications of the obtained results to nonlinear mechanics are presented.

 

Author Biography

  • V. Yu. Slyusarchuk, Nat. Univ. farms and nature management, Rivne

    Василь Юхимович

References

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Published

15.01.2020

Issue

Section

Research articles

How to Cite

Slyusarchuk, V. Yu. “Equations in a Hilbert Space Whose Solution Sets Are Invariant With Respect to a Group Isomorphic to a One-Parameter Group of Unitary Operators”. Ukrains’kyi Matematychnyi Zhurnal, vol. 72, no. 1, Jan. 2020, pp. 86-99, https://umj.imath.kiev.ua/index.php/umj/article/view/687.