Steady-state heat transfer problems have been considered in a composite solid comprising two materials, one, a slab, which forms the bulk of the interior and the other, a plate, which forms a thin layer around the boundary. Through the use of appropriate Green's functions, it is shown that the boundary value problem can be converted into a Fredholm integral equation of the second kind. The inte...

In this paper, we are concerned with the second order self-adjoint boundary value problem at resonance −(p(t)x′(t))′ = f(t, x(t)), t ∈ (0, 1), x′(0) = 0, x(1) = Z 1

We study the asymptotic behaviour of eigenvalues and eigenfunctions 2D vibrating systems with mass density perturbed in a vicinity closed curves. The threshold case which resonance frequencies membrane thin inclusion coincide or closely situated is investigated. eigenvalue problem can be realized as family self-adjoint operators acting on varying Hilbert spaces. However so-called limit operator...

4 Where do orthogonal polynomials come from? 10 Continued fractions . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Padé approximation and rational interpolation . . . . . . . . . . 11 Moment problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Jacobi matrices and spectral theory of self-adjoint operators . . . 13 Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . ....

Examples of symmetric quantum semimartingales are easy to find, but essentially self-adjoint quantum semimartingales have, in general, proved elusive. This is not unexpected since a quantum semimartingale is in some sense an indefinite integral of a family of unbounded operators, and strong conditions are required to ensure that the sum of even two unbounded self-adjoint operators is self-adjoi...

We discuss minisuperspace aspects a non empty Robertson-Walker universe containing scalar matter field. The requirement that the Wheeler-DeWitt (WDW) operator be self adjoint is a key ingredient in constructing the physical Hilbert space and has non-trivial cosmological implications since it is related with the problem of time in quantum cosmology. Namely, if time is parametrized by matter fiel...

Let a pair of self-adjoint operators fA 0;W 0g be such that (a) there is a dense domain D dom(A) \ dom(W ) that _ H = (A +W )jD is semibounded from below (stability domain), (b) the symmetric operator _ H is not essentially self-adjoint (singularity of the perturbation), (c) the Friedrichs extension  of _ A = AjD is maximal with respect to W , i.e., dom(p W )\ ker( _ A I) = f0g, < 0. Let fWng1...

We begin with the definition of a skew-Hermitian form and the corresponding Hermitian symplectic group. We motivate these definitions with a discussion of their relevance to self-adjoint extensions of Hamiltonian operators. In doing so, we introduce the basics of von Neumann’s extension theory. Next, we develop the necessary tools from Hermitian symplectic linear algebra to study self-adjoint e...

The norm convergence of the Trotter{Kato product formula is established with ultimate optimal error bound for the self-adjoint semigroup generated by the operator sum of two self-adjoint operators. A generalization is also given to the operator sum of several self-adjoint operators.

We discuss the division method for subspectra which appears to be one of the key approaches in the study of spectral properties of self-adjoint differential vector-operators, that is operators generated as a direct sum of self-adjoint extensions on an Everitt-Markus-Zettl multi-interval system. In the current work we show how the division method may be applied to obtain the ordered spectral rep...