Riescz basis

On Riescz Bases of Eigenfunction of 2-nd Order Differential Operator with Involution and Integral Boundary Conditions

Authors: Kurdyumov V. P.

Riesz basisness with brackets of the eigen and associated function is proved for a 2-nd order differential operator with involution in the derivatives and with integral boundary conditions. To demonstrate this the spectral problem of the initial operator is reduced to the spectral problem of a 1-st order operator without involution in the 4-dimensional vector-function space.

Riescz Basis Property of Eigen and Associated Functions of Integral Operators with Discontinuous Kernels, Containing Involution

Authors: Kurdyumov V. P., Khromov A. P.

For invertible integral operator which kernel is discontinuous on the diagonals of the unit square Riescz basis property of its eigen and associated functions in L2[0, 1] is proved.