An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...

In this paper we give a complete description of the Fredholm spectrum of the linearized 3D Euler equation in terms of the dynamical spectrum of the cocycle governing the evolution of shortwave perturbations. The argument is based on the pseudo differential representation of the Euler group and an application of an abstract isomorphism theorem for operator C∗-algebras. We further show that for a...

January 2002 Abstract. A convergence model with wealth accumulation subject to i.i.d. random shocks is examined. The transfer function shows what kt+1 wealth at t + 1 would be, given kt, with no shock. It has a positive slope, but its concavity/convexity is indeterminate. The stationary distribution of wealth satis...es a Fredholm integral equation. This distribution can be examined by direct a...

For smooth hyperbolic dynamical systems and smooth weights, we relate Ruelle transfer operators with dynamical Fredholm determinants and dynamical zeta functions: First, we establish bounds for the essential spectral radii of the transfer operator on new spaces of anisotropic distributions, improving our previous results [7]. Then we give a new proof of Kitaev’s [17] lower bound for the radius ...

We consider linear operators and equations with partial integrals in Banach ideal spaces, spaces of vector functions, continuous functions. study the action, regularity, duality, algebras, Fredholm properties, invertibility, spectral properties such operators. describe principal integrals. show that are essentially different compared to usual integral equations. obtain conditions for alternativ...