Spectral Properties for Pseudodifferential Operators via Weighted Modulation Spaces - Askari-Hemmat, A.; Rahbani, Z. (Communications in Mathematics and Applications, 2012)
In this paper we deal with this question: considering spectral representation of a positive trace-class integral operator, if its orthonormal eigenvectors are in modulation space M^p_m? This question actually provide a new framework for studying the connection between operator theory and modulation spaces. Here we use some Schatten class properties of seudodifferential operators to give a positive answer to this question. Also we investigate convergence conditions for eigenvectors of such operators.