We study the resonant set of a two-level Schrödinger operator with a linear conical intersection. This model operator can be decomposed into a direct sum of first order systems on the real halfline. For these ordinary differential systems we locally construct exact WKB solutions, which are connected to global solutions, amongst which are resonant states. The main results are a generalized Bohr-...

In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace operators on unbounded finitely ramified self-similar sets. In this context, this furnishes the first example of a description of the spectral nature of the operator...

A central problem of dynamical systems theory is to identify a reduced description of the dynamical process one can deal easier. In this paper we present a systematic method of identifying those closed sub-systems of a given discrete time dynamical system in the frame of operator theory. It is shown that this problem is closely related to finding invariant sigma algebras of the dynamics. Index ...

Ascending and descending Morse complexes are defined by the critical points and integral lines of a scalar field f defined on a manifold M . They induce a subdivision of M into regions of uniform gradient flow, thus providing a compact description of the topology of M and of the behavior of f over M . We represent the ascending and descending Morse complexes of f as a graph, that we call the Mo...

Symbolic nuclear magnetic resonance (NMR) product operator calculations provide an analytic, intuitive, yet precise description of the time evolution of the density operator during an NMR experiment. NMR experiments are implemented as pulse sequences consisting of short radiofrequency pulses separated by delay periods during which the spin system evolves under the influence of the static extern...

We give a description of all transmutation operators from the Bessel-Struve operator to the second-derivative operator. Next we define and characterize the mean-periodic functions on the space Ᏼ of entire functions and we characterize the continuous linear mappings from Ᏼ into itself which commute with Bessel-Struve operator. 1. Introduction. Let A and B be two differential operators on a linea...

Example 1: Fuel Injector Nozzle Diameters Problem A manufacturer of fuel injector nozzles installs a new digital measuring system. Investigators want to determine how well the new system measures the nozzles. Data set Nozzle.MPJ Description Variable Fuel injector nozzle measured Nozzle Data collection Technicians randomly sample, across all major sources of process variation (machine, time, shi...

For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.

In this paper we give a uni ed description of the archimedean and the totally split degenerate bers of an arithmetic surface, using operator algebras and Connes' theory of spectral triples in noncommutative geometry.

Abstract We give a new class of equivalent norms for modulation spaces by replacing the window short-time Fourier transform Hilbert–Schmidt operator. The main result is applied to Cohen’s time-frequency distributions, Weyl operators and localization operators. In particular, any positive distribution with Schwartz kernel can be used an norm spaces. also obtain description as Wiener amalgam oper...