ON THE REGULARIZATION OF SOME SINGULAR INTEGRAL OPERATORS. NOETHERIAN CRITERIA
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Keywords

singular integral operator, compact operator, regularization.

How to Cite

NEAGU, V. (2020). ON THE REGULARIZATION OF SOME SINGULAR INTEGRAL OPERATORS. NOETHERIAN CRITERIA. Acta Et Commentationes Exact and Natural Sciences, 8(2), 58-69. https://doi.org/10.36120/2587-3644.v8i2.58-69

Abstract

The work is centered on the study of algebra A generated by singular integral operators with shifts with continuous coefficients. Necessary and sufficient conditions are established for operators A to be Noetherian and to admit equivalent regularization in the space (,) Lp . There are constructed regularizators for Noetherian operators. The study is done in the space (, ) Lp with weight ρ(t) = t − tk n k=1 βk and is based on the theory of Ghelfand [1] concerning Banach algebras. The main results of this work were presented at the 9-th Congress of Romanian  Mathematicians, which took place in Galați, 2019.

2010 Mathematics Subject Classification: 34G10.

https://doi.org/10.36120/2587-3644.v8i2.58-69
pdf (Русский)
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