On Taylor coefficients of Cauchy-type integrals of finite complex measures

Abstract

Boundary values of Cauchy-type integrals of finite complex measures given on a unit circle, generally speaking, are not Lebesgue integrable, and therefore at expansion of Cauchy-type integrals in Taylor series, the expansion coefficients cannot be expressed by boundary values using the Lebesgue integral. In this paper, using the notion of A-integration and N-integration, we get a formula for calculating the Taylor expansion coefficients of Cauchy-type integrals of finite complex measures.

Keywords:

• Cauchy-type integral
• non-tangential boundary values
• Taylor expansion
• Taylor coefficients
• A-integral
• N-integration

AMS Subject Classifications:

• 26A39
• 28A50
• 30E20
• 30E25
• 41A58

Notes

No potential conflict of interest was reported by the author.