Spectral decomposition with monotonic spectral resolvents

Noncommutative Spectral Decomposition with Quasideterminant

We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative CayleyHamilton’s theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it h...

Predicting stratigraphy with spectral decomposition

Interpretation of subsurface geology is greatly enhanced by 3-D seismic data, and this accounts for its ubiquity in today’s search for hydrocarbons. Seismic interpretation has two fundamental disciplines at its core: seismic geomorphology and seismic stratigraphy. Plan views allow the explorationist to apply principles of geomorphology, based on analogies with modern sedimentary systems, to int...

Entropy monotonic spectral method for Boltzmann equation

We propose a spectral method that discretizes the Boltzmann collision operator and satisfies a discrete version of the H-theorem. The method is obtained by modifying the existing Fourier spectral method to match a classical form of the discrete velocity method. It preserves the positivity of the solution on the Fourier collocation points and as a result satisfies the H-theorem. The fast algorit...

ON DUALITY AND SPECTRAL PROPERTIES OF (a, k)-REGULARIZED RESOLVENTS

We construct a duality theory for (a, k) regularized resolvents, extending some of the known theorems for dual semigroups. We present several classes of spaces, which in the semigroup case correspond to the Favard class and the sun-dual space. By duality arguments spectral inclusions theorems for regularized resolvents are also obtained.

Spectral properties of pseudo-resolvents under structured perturbations