Some partial differential Volterra equation problems arising in viscoelasticity
Let Ω= [a, b] × [c, d] and T 1, T 2 be partial integral operators in (Ω): (T 1 f)(x, y) = k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = k 2(x, ts, y)f(t, y)dt where k 1 and k 2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT 1, τ ∈ ℂ and E−τT 2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra of bounded...
Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk or on the Segal-Bargmann space over . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression of A to the linear span of the monomials . Unfortunately, in general the spectrum of does not mimic the spectrum of A as...