ON A FAMILY OF GENERALIZED SHIFT OPERATORS
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In this paper a special representation of the algebra of differential operators is constructed. Using this representation a family of generalized shift operators is studied for which the th order infinitesimal operators form an arbitrary Lie algebra. Systems of differential equations with bounded operator coefficients, having th order infinitesimal operators in the left sides, are also studied.Bibliography: 4 titles.
Integral, integro-differential, and pseudodifferential operators, General theory of partial differential operators, Groups and semigroups of linear operators, their generalizations and applications, Linear operators in algebras, General theory of ordinary differential operators, Representations of Lie and linear algebraic groups over real fields: analytic methods
Integral, integro-differential, and pseudodifferential operators, General theory of partial differential operators, Groups and semigroups of linear operators, their generalizations and applications, Linear operators in algebras, General theory of ordinary differential operators, Representations of Lie and linear algebraic groups over real fields: analytic methods
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