ALGEBRE ECHIVALENTE DE OPERATORI INTEGRALI SINGULARI. CRITERII NOETHERIENE

Diana BÂCLEA, Vasile NEAGU

Abstract


În prezenta lucrare sunt stabilite condiții necesare și suficiente în care operatorii integrali singulari cu translații de tip Carleman sunt noetherieni, se determină simbolul și se calculează indicele acestor operatori. Aceste rezultate sunt obținute datorită studiului algebrei generate de acești operatori în spațiul  cu o anumită pondere, aleasă astfel încât să asigure continuitatea operatorilor. În studiul algebrei respective un rol important are noțiunea de echivalență a algebrelor Banach, introdusă de către matematicienii I.Gohberg și N.Krupnik.

EQUIVALENT ALGEBRAS OF SINGULAR INTEGRAL OPERATORS. NOETHERIAN CRITERIONS

In the present work there are established necessary and sufficient conditions under which sungular integral operators with shift of Carleman tipe are Notherian, the symbol of these operators is determined and index of these operators is calculated. These results are obtained due to the study of the algebra, generated by these operators in the space  with a certain weight, chosen in such a way, that continuity of operators is ensured. In the study of this algebra an important role has the notion of equivalence of Banach algebras, introduced by mathematicians I. Gohberg and N.Krupnik.


Keywords


singular integral operator, noetherian operator, symbol.

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References


KRAVCHENKO, V., LITVINCHIUK, G. Introduction to the Theory of Singular Integral Operators with Shift. Kluwer, 2012.

KRUPNIK, N., NEAGU, V. On singular operators with shift in the case of piecewise Lyapunov contour. In: Soobsch. Akad. Nauk Gruz. SSR, 1974, no76, p.25-28 (Russian).

KRUPNIK, N., NEAGU, V. Singular integral operators with a shift along a piecewise Lyapunov contour. In: Izv. Vyssh. Uchebn. Zaved., Mat., 1975, no6, p.60-72 (Russian).

NEAGU, V. Singular integral operators. The case of an unlimited contour. In: Revue analyse numérique et de théorie de approximation (Académie Roumaine), tome XXXIV, 2005, no2, p.151-168.

DUDUCHAVA, R. Convolution integral operators on a quadrant with discontinuous symbols. In: Izv. Akad. Nauk SSSR. Ser. Mat., 1976, no40:2, p.388-412 (Russian).

GOHBERG, I., KRUPNIK, N. One-dimensional linear singular integral equations. Vol.I. Operator Theory. Basel-Boston –Stuttgart, 1992.

GOHBERG, I., KRUPNIK, N. On certain one-dimensional singular integral operators with a shift. In: Izv. Akad. Nauk Arm. SSR, 1973, no1, p.3-12 (Russian).

KRUPNIK, N. Banach algebras with symbol and singular integral operators. Operator Theory: Advances and Applications (Birkhäuser), 26, 1987.

KARAPETYANTS, N., SAMKO, S. Equations with Involutive Operators and Their Applications. Operator Theory: Advances and Applications (Birkhäuser), 2005.

NYAGU, V. The symbol of singular integral operators with conjugation the case of piecewise Lyapunov contour. American Math. Society, 1983, vol.27, no1, p.173-176.

CASTROL, R. Explicit solutions of Cauchy singular integral equations with weighted Carleman shift. In: J. Math. Anal. And Appl., 2010, vol.371, no1, p.128-133.


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