An analog of a Nevanlinna fundamental theorem for real functions

Abstract

In this article we study a “generalized oscillation problem” for real smooth function f(x), x ∈ (a, b). Namely we obtain above bounds for the magnitude

, where N(a, b, f − A _ν) is the number of solutions f − A _ν in ( a, b ) and

, is a totality of pairwise different real numbers. The obtained inequality is in some aspects similar to that of the second fundamental theorem in Nevanlinna value distribution theory.

Keywords:

• Zeros of real functions
• Gamma-lines
• Nevanlinna theory
• Mathematics Subject Classifications 2000: 26A99
• 26C99
• 30D30
• 30C99

Notes

Dedicated to Heinrich Begehr on the occasion of his 65th birthday.

Email: [email protected]

Email: [email protected]

Additional information

Notes on contributors

G. A. Barsegian *

Dedicated to Heinrich Begehr on the occasion of his 65th birthday. Email: [email protected]