Projection Method in the Theory of Integral Operators with Homogeneous Kernels

To the Memory of Professor Nikolai Karapetiants: Life and Scientific Heritage

“…Later, the integral operators, whose kernels are homogeneous of degree (−n) and invariant under the rotation group SO(n), were studied by N. K. Karapetiants and O. G. Avsyankin. For such operators, the criteria for invertibility and the Fredholm property were obtained, the Banach algebras generated by these operators were studied, the conditions for the projection method to be applied were found and the limiting behavior of the spectral characteristics of the truncated operators was described (see [8][9][10][11][12][13]).…”

Multidimensional integral operators with bihomogeneous kernels: A projection method and pseudospectra

“…The results of this research for multidimensional integral operators with homogeneous kernels are reflected in [5][6][7].…”