On the determinacy of complex Jacobi matrices

DETERMINACY OF COMPLEX JACOBI MATRICES 21 Introdu

Comparative study on solving fractional differential equations via shifted Jacobi collocation method

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear Integro-Differential Equations

‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matr...

Two modified Jacobi methods for M-matrices

Measures with Finite Index of Determinacy or a Mathematical Model for Dr. Jekyll and Mr. Hyde

In this note measures with finite index of determinacy (i.e. determinate measures μ for which there exists a polynomial p such that |p|2μ is indeterminate) are characterizated in terms of the operator associated to its Jacobi matrix. Using this characterization, we show that such determinate measures with finite index of determinacy (Jekyll) turn out to be indeterminate (Hyde) when considered a...