Operators of solution for convolution equations


We prove that the existence of a solution operator for a convolution operator from the space of ultradifferntiable functions to the corresponding space of ultradistributions is equivalent to the existence of a continuous solution operator in the space of functions. Our results are in the spirit of a classical characterization of the surjectivity of convolution operators due to Hörmander. The behaviour of a fixed convolution operator in different classes of ultradifferentiable functions of Beurling type concerning the existence of a continuous linear right inverse is also considered.

DOI Code: 10.1285/i15900932v17p1

Keywords: Spaces of ultradifferentiable functions; Convolution operators; Continuous linear right inverse

Classification: 46F05; 46E10; 46F10; 35R50

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