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No abstract uploaded!

A new elementary approach to uniform resolvent estimates of the Carleman-type is developed. Schatten-von Neumann's $$\mathfrak{S}_p $$ perturbations of self-adjoint and unitary operators are considered. Examples of typical growth are provided.

No abstract uploaded!

The sine(hyperbolic)-Gordon hierarchy is shown to be the extension of the modified Korteweg-de Vries (MKdV) hierarchy in the integrodifferential algebra extending the standard differential algebra by means of one antiderivative. The characterization by vanishing residues of the MKdV hierarchy yields the same characterization of the sine(hyperbolic)-Gordon hierarchy in the integrodifferential algebra.