Raphael Kapanadze

Factorization of Matrix-functions and Regularization of Singular Integral Operators on Manifolds with Boundary

The problem of expansion of positively homogeneous matrix-functions is studied. Certain algebraic, differential and asymptotic properties of cofactors are established. The results obtained are used to investigate the problem of regularization of singular integral operators on manifolds with boundary in H\"{o}lder spaces with weight.

Mathematics Subject Classification: 45F15, 35S15.

Key words and phrases: Factorization of matrix-functions, asymptotic properties of expansion cofactors, strongly elliptic symbols, singular integral operators on manifolds with boundary, H\"{o}lder spaces with weight.