Inversion of matrix convolution type operators with symmetry

L.P. Castro and F.-O. Speck

Abstract: We consider matrix convolution type operators that carry a certain symmetry due to the presence of even or odd extensions. The study is motivated by mathematical physics applications where this kind of operators appears. In connection with this interest, a class of Hölder continuous Fourier symbols is taken into consideration. The main result consists of sufficient conditions for the invertibility of such operators including a presentation of the corresponding inverse operator in terms of an asymmetric factorization of the symbol matrix. Moreover the asymptotic behavior of the factors is analyzed.

Keywords: convolution type operator; Wiener--Hopf--Hankel operator; factorization; invertibility; Hölder continuity.

Classification (MSC2000): 47B35, 47A68.

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