Mathematical Analysis

Faculty with research interests in analysis are Qingying Bu and Erwin Diaz Mina.

Mathematical analysis, often known simply as analysis, is a core branch of mathematics that developed from calculus and, broadly speaking, investigates questions where a notion of “nearness” plays a central role, often involving limiting processes and functions with some degree of continuity. Classical topics studied in analysis include the continuity, differentiability and integrability of functions of a real or a complex variable, the convergence of numerical or functional sequences and series in Euclidean and abstract topological spaces, and the properties of spaces of functions that share some relevant attributes. Some subfields of analysis are calculus, real and complex analysis, differential equations, harmonic analysis, functional analysis, measure and integration, approximation theory, numerical analysis, and potential theory. Mathematical analysis has tremendous applications in other disciplines such as physics, engineering, signal processing, and economics.

Dr. Bu’s research interests involve Functional Analysis, especially in Banach space theory, multilinear operators and homogeneous polynomials on Banach spaces, positive multilinear operators and homogeneous polynomials on Banach lattices, tensor products on Banach spaces, and positive tensor products on Banach lattices.

Dr. Mina-Diaz’s research is in the area of approximation theory, primarily in the complex plane. He has made important contributions to the asymptotic theory of orthogonal polynomials with respect to planar-type measures, and has also worked on the topics of orthogonal polynomials over the unit circle and over more general analytic curves, convergence of quadrature formulas, universality of conditional measures of the sine point process, reproducing kernels and zero divisors in Bergman spaces, and optimal energy points on the unit circle. Mina-Diaz research makes use of real and complex analysis, functional analysis, and potential theory.