We consider the problem of finding a sharp constant in the approximation of continuous functions by linear methods. The best constant is obtained for the approximation by the second-order Cesàro means of classes of Lipschitz continuous periodic functions.
We consider an operator represented by the sum of a series in the values of the resolvent of a densely defined closed operator in a complex Banach space. We describe the left inverse for this operator, apply this result to regularization of equations of the first kind, and consider several examples.
We apply the inverse scattering method to integrating the loaded Korteweg–de Vries equation with a self-consistent source of integral type in the class of rapidly decreasing complex-valued functions.
We consider mixed boundary value problems for one pseudohyperbolic equation in a quarter plane. We assume that the boundary value problems satisfy the Lopatinskiĭ condition. We prove theorems on unique solvability in anisotropic Sobolev spaces with exponential weight and establish some estimates for the solutions.
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