Related papers: Matrix methods for wave equations
We introduce an abstract setting that allows to discuss wave equations with time-dependent boundary conditions by means of operator matrices. We show that such problems are well-posed if and only if certain perturbations of the same…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(-A)^{1/2} generates a bounded C_0-group. The proof uses a transference principle for cosine functions.
In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and…
General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are…
We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and…
In this article we consider means of positive operators on a Hilbert space. We extend the theory of matrix power means to arbitrary operator means in the sense of Kubo-Ando. The basis of the extension is relying on ideas coming from…
An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered.…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
This paper considers two frequently used matrix representations -- what we call the $\chi$- and $\mathcal{S}$-matrices -- of a quantum operation and their applications. The matrices defined with respect to an arbitrary operator basis, that…
Partial wave decomposition is one of the main tools within the modern S-matrix studies. We present a method to compute partial waves for $2\to2$ scattering of spinning particles in arbitrary spacetime dimension. We identify partial waves as…
Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
In this paper we study the stability properties of strongly continuous semigroups generated by block operator matrices. We consider triangular and full operator matrices whose diagonal operator blocks generate polynomially stable…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We…