Generalized γ-generating matrices

Abstract

The classes of right and left γ-generating matrices were introduced by D. Z. Arov in the 1980s. These matrices play an important role in the description of solutions of the indeterminate Nehari problem. In the present paper, the classes of the so-called generalized right and left γ-generating matrices, being resolvent matrices of the Nehari–Takagi problem, are introduced. For matrices of these classes, some factorization theorems are proved, and the connection between the class of generalized γ-generating matrices and the class of generalized j_pq-inner matrix valued functions is found. Subclasses of singular, regular, and strongly regular generalized -generating matrices are introduced and studied.