Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
On an algebraic method in the study of integral equations with shift.
Authors: Vasile Neaga
generated by singular integral operators with shifts with continuous coefficients. We determine the set of maximal ideals of quotient
algebra 
, 
, with respect to the ideal of compact operators. Prove that the bicompact of maximal ideals of is isomorphic to the topological product (Γ × j) × (Γ × k), where j = ± 1 and k = ± 1 Necessary and sufficient condition are established for operators of to be noetherian and to admit equivalent regularization in space Lp(Γ, ρ), regularizators for noetherian operators are constructed. The study is done in the space Lp(Γ, ρ) with weight 
and is based on the theory of Ghelfand [1] concerning Banach algebras.
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Abstract
The work is centred on the sdudy of algebra generated by singular integral operators with shifts with continuous coefficients. We determine the set of maximal ideals of quotient
algebra , , with respect to the ideal of compact operators. Prove that the bicompact of maximal ideals of is isomorphic to the topological product (Γ × j) × (Γ × k), where j = ± 1 and k = ± 1 Necessary and sufficient condition are established for operators of to be noetherian and to admit equivalent regularization in space Lp(Γ, ρ), regularizators for noetherian operators are constructed. The study is done in the space Lp(Γ, ρ) with weight and is based on the theory of Ghelfand [1] concerning Banach algebras.
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Contents
- Quotient rings of pseudonormed rings.
- Numerical treatment of the Kendall equation in the analysis of priority queueing systems.
- On the Division of Abstract Manifolds in Cubes.
- The numerical analysis of the tense condition of a solid body with the asymmetrical tensor of strains.
- On the coproducts of cyclics in commutative modular and semisimple group rings.
- Commutative Moufang loops with maximum conditions for subloops.
- Discontinuous term of the distribution for Markovian random evolution in R3.
- On an algebraic method in the study of integral equations with shift.
- On a family of Hamiltonian cubic planar differential systems.
- The solvability and properties of solutions of an integral convolutional equation.
- On commutative Moufang loops with some restrictions for subgroups of its multiplication groups.
- The property of universality for some monoid algebras over non-commutative rings.
- Junior spatial groups of (22'1)-symmetry.
