# Accession Number:

## AD0688917

# Title:

## ON THE SOLUTION OF A GENERALIZED WIENER-HOPF EQUATION,

# Descriptive Note:

# Corporate Author:

## ILLINOIS UNIV URBANA DEPT OF ELECTRICAL ENGINEERING

# Report Date:

## 1969-04-01

# Pagination or Media Count:

## 29.0

# Abstract:

The paper deals with the generalized Wiener-Hopf equation Galpha Xalpha Halpha X-alpha - Y-alpha psiialpha 0, tau sub 1 tau tau sub 2 where alpha sigma i tau is a complex variable Galpha, Halpha, and psi ialpha are known functions and, Xalpha, Y-alpha are unknowns, analytic in upper and lower half planes respectively, as indicated by their respective subscripts. This type of equation arises in a class of boundary value problems in electromagnetic theory the geometries of which may be described as modified Wiener-Hopf type. The method of approach, which is fundamentally different than those currently available in the literature, is based on a pairing of singularities in the complex alpha-plane. This leads to a functional equation which is exactly solvable in its asymptotic form. The knowledge of this solution permits one to employ one of several rapidly converging numerical procedures available in the literature for a more accurate solution. Two examples illustrating the application of the procedure are included in the paper. Author

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Radiofrequency Wave Propagation