A theory of composites perspective on matrix valued Stieltjes functions

On Ap-henstock-stieltjes Integral of Interval-valued Functions

In this paper we introduce the interval-valued APHenstock-Stieltjes integral and investigate some properties of the these integrals.

On Matrix-valued Herglotz Functions

We provide a comprehensive analysis of matrix-valued Herglotz functions and illustrate their applications in the spectral theory of self-adjoint Hamiltonian systems including matrix-valued Schrödinger and Dirac-type operators. Special emphasis is devoted to appropriate matrix-valued extensions of the well-known Aronszajn-Donoghue theory concerning support properties of measures in their Nevanli...

A Study on Nonsymmetric Matrix-valued Functions

2009 Acknowledgements I would like to express my sincere gratitude to my supervisor, Professor Sun Defeng for all of his guidance, encouragement and support. He taught me how to do research and did it with great care and patience. his patient guidance and great help. I would also like to acknowledge National University of Singapore for providing me the financial support and the pleasant environ...

On differentiability of symmetric matrix valued functions

With every real valued function, of a real argument, can be associated a matrix function mapping a linear space of symmetric matrices into itself. In this paper we study directional differentiability properties of such matrix functions associated with directionally differentiable real valued functions. In particular, we show that matrix valued functions inherit semismooth properties of the corr...

The theory of matrix-valued multiresolution analysis frames