Ahmed MuhammadSalahaddin University - Erbil | SUH · Department of Mathematics
Ahmed Muhammad
PhD
About
10
Publications
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Introduction
My research lie in the fields of operator theory and functional analysis.
I am particularly interested in numerical range of operator matrices, numerical range of operator polynomials, c-numerical range of operator matrices, q-numerical range of operator matrices, q-numerical range of operator polynomials, S-numerical range of operator matrices, S-numerical range of operator polynomials and quadratic numerical range of block operator matrices (theory and numerics).
Publications
Publications (10)
Understanding the behaviour of nonlinear dynamical systems is crucial in epidemiological modelling. Stability analysis is one of the important concepts in assessing the qualitative behaviour of such systems. This technique has been widely implemented on deterministic models involving ordinary differential equations (ODEs). Nevertheless, the applica...
In this paper, some established properties and results on numerical range and quadratic numerical range of block operator matrices are studied and compared. These results and properties are then applied to compute both ranges for block operator matrices of self-adjoint as well as non-self-adjoint types in the complex Hilbert space.
A linear operator on a Hilbert space may be approximated by finite matrices choosing an orthonormal basis of the Hilbert space. In this paper we establish an approximation of the q-numerical range of a bounded and an unbounded polynomial operator by variational methods. Applications to Hain-Lüst operator and Stokes operator are also given.
A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of thez Hilbert space. In this paper, we establish an approximation of the -numerical range of bounded and unbounnded operator matrices by variational methods. Application to Schrödinger operator, Stokes operator, and Hain-Lüst operator is...
In this paper, we consider the problem of computing the c-numerical range numerically for block differential operators, particularly these of Schrödinger type, Hain–Lüst type, and Stokes type.
The quadratic numerical range (QNR) was introduced by Langer and Tretter [Spectral decomposition of some non-self-adjoint block operator matrices, J. Oper. Theory 39 (1998), pp. 339–359] as a tool for estimating the spectra of operators which admit a natural block matrix representation with respect to a decomposition of the underlying Hilbert space...
In this paper we establish an approximation of the quadratic numerical range of bounded and unbounded block operator matrices by variational methods. Applications to Hain–Lüst operators are given.
