Spectral problem for the Dirac operator with regular but not strongly boundary conditions and complex-valued potential summable over a finite interval is considered. The purpose of this paper to find under which root function system forms usual Riesz basis rather than parentheses.

In this paper, we show how to construct an orthonormal basis from Riesz by assuming that the fractional translates of a single function in core subspace multiresolution analysis form instead basis. definition analysis, intersection triviality condition follows other conditions. Furthermore, union density also under assumption Fourier transform scaling is continuous at 0. At culmination, provide...

Recently, we presented a new image pyramid, called the Riesz pyramid, that uses the Riesz transform to manipulate the phase in non-oriented sub-bands of an image sequence to produce real-time motion-magnified videos. In this report we give a quaternionic formulation of the Riesz pyramid, and show how several seemingly heuristic choices in how to use the Riesz transform for phase-based video mag...

In this paper we construct Powell–Sabin spline multiwavelets on the hexagonal lattice in a shift-invariant setting. This allows us to use Fourier techniques to study the range of the smoothness parameter s for which the wavelet basis is a Riesz basis in the Sobolev space H(R), and we find that 0.431898 < s < 5/2. For those s, discretizations of H -elliptic problems with respect to the wavelet b...

We prove that for any convex polytope $\Omega \subset \mathbb{R}^d$ which is centrally symmetric and whose faces of all dimensions are also symmetric, there exists a Riesz basis exponential functions in the space $L^2(\Omega)$. The result new $d$ greater than one.

In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...