相关论文: The Wavelet Galerkin Operator
On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…
We introduce a multitree-based adaptive wavelet Galerkin algorithm {for} space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems. It is shown that the method converges with the best…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
We study the connection between *-representations of algebras associated with graphs, locally-scalar graph representations and the problem about the spectrum of a sum of two Hermitian operators. For algebras associated with Dynkin graphs we…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
We present an adaptive wavelet Galerkin method for transient heat conduction in heterogeneous composite materials. The approach combines multiresolution wavelet bases with an implicit time discretization to efficiently resolve sharp…
In this work we develop a theory of Vessels. This object arises in the study of overdetermined 2D systems invariant in one of the variables, which are usually called time invariant. To each overdetermined time invariant 2D systems there is…
One may obtain, using operator transformations, algebraic relations between the Fourier transforms of the causal propagators of different exactly solvable potentials. These relations are derived for the shape invariant potentials. Also,…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets,…
We show that the orthogonal projection operator onto the range of the adjoint of a linear operator $T$ can be represented as $UT,$ where $U$ is an invertible linear operator. Using this representation we obtain a decomposition of a Normal…
We construct $R$-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They…
We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…
This paper provides a description of the spectrum of diagonal perturbation of weighted shift operator acting on a separable Hilbert space.
We discuss the polar in symbol space to hypoelliptic and partially hypoelliptic operators, assuming a transmission property related to a rectifiable boundary and using a representation based on two scalar products.
Markov expanding maps, a class of simple chaotic systems, are commonly used as models for chaotic dynamics, but existing numerical methods to study long-time statistical properties such as invariant measures have a poor trade-off between…
The theory of quaternionic operators has applications in several different fields such as quantum mechanics, fractional evolution problems, and quaternionic Schur analysis, just to name a few. The main difference between complex and…
The problem of identifying and reconstructing operators from a diagonal of the Gabor matrix is considered. The framework of Quantum Time--Frequency Analysis is used, wherein this problem is equivalent to the discretisation of the diagonal…
Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…