Authors: Vasile Neaga
Abstract
The work is centred on the sdudy of algebra
![](/files/basm/y2006-n2/y2006-n2-f1.png)
generated by singular integral operators with shifts with continuous coefficients. We determine the set of maximal ideals of quotient
algebra
![](/files/basm/y2006-n2/y2006-n2-f2.png)
,
![](/files/basm/y2006-n2/y2006-n2-f3.png)
, with respect to the ideal of compact operators. Prove that the bicompact of maximal ideals of
![](/files/basm/y2006-n2/y2006-n2-f2.png)
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
![](/files/basm/y2006-n2/y2006-n2-f1.png)
to be noetherian and to admit equivalent regularization in space L
p(Γ, ρ), regularizators for noetherian operators are constructed. The study is done in the space L
p(Γ, ρ) with weight
![](/files/basm/y2006-n2/y2006-n2-f4.png)
and is based on the theory of Ghelfand [1] concerning Banach algebras.
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