Learn More
In this paper we study weighted Hardy-Sobolev spaces of vector valued functions analytic on double-napped cones of the complex plane. We introduce these spaces as a tool for complex scaling of linear ordinary differential equations with dilation analytic unbounded operator coefficients. As examples we consider boundary value problems in cylindrical domains(More)
We construct a perfectly matched absorbing layer for stationary Schrödinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite length and show that solution to this problem approximates a solution to the original problem with an error that(More)
In this paper we develop the complex scaling method for the Euclidean Dirichlet Laplacian in a domain with asymptotically cylindrical end. We prove an analog of the Aguilar-Balslev-Combes theorem, and construct the resolvent meromorphic continuation across the essential spectrum to some Riemann surface. We show that the non-threshold eigenfunctions decay(More)
  • 1