Generalized factorization for a class of 2 × 2 matrix functions with non-rational entries

Abstract

The problems of existence and calculation of a generalized factorization for a class of non-rational matrix functions are examined. The class considered, which consist of 2 × 2 matrix functions whose elements are of form , has not, up to now, been studied and existing methods of factorization do not apply to it. Such matrix functions may appear e.g. in relation to boundary-value problems involving fourth order differential operators (α =1/4). The authors derive necessary and sufficient conditions for the existence of a canonical factorization and give explicit formulas for the factors.

Keywords:

• Wiener-Hopf factorization
• generalized factorization
• Weiner-Hopf operators

AMS:

• 47A68
• 47B35