Tony Hill
abstract:
This paper considers the factorization of elliptic symbols which can be
represented by matrix-valued functions. Our starting point is a Fundamental
Factorization Theorem, due to Budjanu and Gohberg [2]. We critically examine
the work of Shamir [15] together with some corrections and improvements as
proposed by Duduchava [6]. As an integral part of this work, we give a new and
detailed proof that certain sub-algebras of the Wiener algebra on the real line
satisfy a sufficient condition for a right standard factorization. Moreover,
assuming only the Fundamental Factorization Theorem, we provide a complete proof
of an important result from Shargorodsky [16], on the factorization of an
elliptic homogeneous matrix-valued function, useful in the context of the
inversion of elliptic systems of multidimensional singular integral operators in
a half-space.
Mathematics Subject Classification: 65N80, 65N12, 65N35
Key words and phrases: Fundamental solution method, adaptive cross approximation, collocation, condition numbers