In this thesis we deal with the degree of ill-posedness of linear operator equations Bx = y in Hilbert spaces X =Y = L2(0,1), where B may be decomposed into a compact linear integral operator J with a well-known decay rate of singular values and a multiplication operator M. This case occurs for example for nonlinear operator equations F(x) = y, where F = N ◦J. Then the local degree of ill-posed...

The linearized collision operator of the Boltzmann equation can in a natural way be written as sum positive multiplication operator, frequency, and an integral operator. Compactness for monatomic single species is classical result, while corresponding result mixtures more recently obtained. In this work compactness polyatomic species, where polyatomicity modeled by discrete internal energy vari...

Let R be a commutative ring. An R-module M is called co-multiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that co-multiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofco-multiplication rings. In additio...

We prove that the hierarchy of higher antibrackets (aka higher Koszul brackets, aka Koszul braces) of a linear operator ∆ on a commutative superalgebra can be defined by some universal formulas involving iterated Nijenhuis–Richardson brackets having as arguments ∆ and the multiplication operators. As a byproduct, we can immediately extend higher antibrackets to noncommutative algebras in a way ...

We prove that the only rearrangement invariant (r.i.) spaces for which there exists a crossnorm verifying that the tensor product of these spaces preserves the “natural” r.i. space structure, in the sense that it makes the multiplication operator B a topological isomorphism, are the Lp spaces.

In this paper, we obtain some characterizations of the boundedness and compactness of the products of the radial derivative and multiplication operator RMu between mixed norm spaces H(p, q, φ) and Zygmund-type spaces on the unit ball. Mathematics subject classification (2010): 47B38, 47G10, 32A10, 32A18.

We study the application of the coherent-state path integral as a numerical tool for wave-packet propagation. The numerical evaluation of path integrals is reduced to a matrix-vector multiplication scheme. Together with a split-operator technique we apply our method to a time-dependent double-well potential.

Abstract We study the convergence of a family numerical integration methods where is formulated as finite matrix approximation to multiplication operator. For bounded functions, has already been established using theory strong operator convergence. In this article, we consider unbounded functions and domains which pose several difficulties compared case. A natural choice method for resolvent pr...

Real linear operators arise in a range of applications of mathematical physics. In this paper, basic properties of real linear operators are studied and their spectral theory is developed. Suitable extensions of classical operator theoretic concepts are introduced. Providing a concrete class, real linear multiplication operators are investigated and, motivated by the Beltrami equation, related ...

We consider the nonstandard constrained KP (ncKP) hierarchy which is obtained from the multi-constraint KP hierarchy by gauge transformation. The second Hamiltonian structure of the ncKP hierarchy can be simplified by factorizing the Lax operator into multiplication form, thus the generalized Miura transformation is obtained. We also discuss the free field realization of the associated W-algebra.