Analytic functions, also known as holomorphic functions, form the cornerstone of complex analysis, widely studied for their elegant properties and deep connections in both pure and applied mathematics ...

For a fixed nonnegative integer m, an analytic map φ and an analytic function ψ the generalized integration operator I φ , ψ m is defined by I φ , ψ m f z = ∫ 0 z f m φ ζ ψ ζ d ζ for X-valued analytic ...

This course will introduce you to the theory of functions of complex variables, which is a core area of mathematics. It is a basic tool in many mathematical theories. We will cover complex numbers and ...

The Applied Mathematics Program is open to those students who have earned a B.S. degree in engineering, science, or mathematics, provided that the student has completed a program in undergraduate ...

Random analytic functions are a fundamental object of study in modern complex analysis and probability theory. These functions, often defined through power series with random coefficients, exhibit ...

Let R be a hyperbolic Riemann surface embedded in a compact Riemann surface of genus g and let f be an analytic function mapping R into R, f not the identity function. Then f has as most 2g + 2 ...