The Zeros of Quasi-Analytic Functions

Zeros of Random Analytic Functions

Zeros of Random Analytic Functions The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of generality. We study zeros of random analytic functions in one complex variable. It is known that there is a one parameter family o...

Quasi-analytic Vectors and Quasi-analytic Functions

On the Distributions of the Zeros of Certain Analytic Functions.

where J and N are positive integers, and the X's are real or complex constants. It is assumed that we do not have XON = XiN = .. = XJN, and that we do not have XOn = Xln = . . . = )kXj * Ofor any n < N. It is also assumed that no two terms in the right-hand member of (1) are identical or differ only by a constant factor. The work reported here is essentially a generalization, in one direction, ...

The Calculation of Zeros of Polynomials and Analytic Functions

On the Zeros of Polynomials and Related Analytic Functions

Let P(z) be a polynomial of degree n with real or complex coefficients, In this paper we obtain a ring shaped region containing all the zeros of P( z), Our results include, as special cases, several known extensions of Enestrom-Kakeya theorem on the zeros of a polynomiaL We shall also obtain zero free regions for certain class of analytic functions.