Qualitative Assessment of Certain Spectral Analysis Methods

Spectral Analysis of Certain Schrödinger Operators

The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey– Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynom...

Qualitative Analysis Methods

Advanced Spectral Analysis Methods

The purpose of time-series analysis is to detect basic properties of the system that engenders a time series. The hope of predicting the system's future evolution is closely related to the possibility of such detection. The most easily predictable components of a system's evolution are the regular, deterministic ones; hence we look for trends and periodic oscillations. In doing so, it is often ...

Qualitative analysis of certain generalized classes of quadratic oscillator systems

We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by C. Quesne [J.Math.Phys.56,012903 (2015)]. By performing a local analysis of the governing potentials we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ, the other po...

Ergodic and Spectral Analysis of Certain Infinite Measure Preserving Transformations

0. Introduction. Throughout this paper T will denote a measure preserving transformation on a cr-finite infinite measure space (X, (B, m) which is point isomorphic with the Lebesgue measure space of the real line. Unless otherwise stated, T will be one-one. Equations involving functions or sets will always be interpreted modulo sets of measure zero. T is said to be ergodic if T~1E = E, ££(B, im...