Open AccessREGULARIZATION OF SOME PERTURBED INTEGRAL OPERATORS IN THE SPACES Lp
Author(s) -
Vasile Neagu
Publication year - 2021
Publication title -
žurnal občislûvalʹnoï ta prikladnoï matematiki
Language(s) - English
Resource type - Journals
eISSN - 2706-9699
pISSN - 2706-9680
DOI - 10.17721/2706-9699.2021.1.22
Subject(s) - mathematics , gravitational singularity , fourier integral operator , operator (biology) , cauchy distribution , connection (principal bundle) , kernel (algebra) , pure mathematics , regularization (linguistics) , operator theory , mathematical analysis , point (geometry) , algebra over a field , computer science , geometry , biochemistry , chemistry , repressor , artificial intelligence , transcription factor , gene
The article presents some generalizations and refinements of the article [1]: examples of integral (non-compact) operators with point wise singularities which are admissible perturbations of the Noetherian operators are constructed; a connection between the regularizes of the perturbed and original operators is established and the equality between the indices of the perturbed and the original operators is proved. The presented results are based on the formulas obtained in this paper for the composition of an operator with the Cauchy kernel and the operators with point wise singularities.