For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed inverse spectral problem is studied, and the description of the space of its solutions is given. We apply the developed technique to give sufficient conditions for...

Using the inverse spectral theory of the nonlinear Schrödinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the JONSWAP spectrum with the proximity to homoclinic solutions of the NLS equation. We find in numerical simulations of the NLS equation that rogue waves develop for JONSWAP initial data that is “near” NLS homoclinic data, while rogue ...

We present a method for extracting the electron-boson spectral function a2Fsvd from infrared and photoemission data. This procedure is based on inverse theory and will be shown to be superior to previous techniques. Numerical implementation of the algorithm is presented in detail and then used to accurately determine the doping and temperature dependence of the spectral function in several fami...

This paper provides a full controlled version of algebraic K-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem describing the behavior of the inverse limit as the control parameter goes to 0. There is a careful treatment of spectral cosheaf homology and related tools, includi...

We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of mapping spaces and another which is cosimplicial. These models are homotopy equivalent to the corresponding knot spaces when the dimension of the ambient manifold is greater than three, and there are spectral sequences with identifiable...

It is shown, using methods of inverse-spectral theory, that there exist Schrödinger operators on the line with fairly general spectral features. Thus, for instance, it follows from the main theorem, that if 0 < α < 1 is arbitrary, and if Σ is any perfect subset of (−∞, 0] with Hausdorff dimension α, then there exist potentials q j , j = 1, 2 such that the associated Schrödinger operators H j ar...