*Correspondence: [email protected] Department of Mathematics, Binzhou University, Shandong, 256603, P.R. China Abstract The square iterative roots for strictly monotonic and upper semicontinuous functions with one set-valued point were fully described in (Li et al. in Publ. Math. (Debr.) 75:203-220, 2009). As a continuation, we study both strictly monotonic and nonmonotonic multifunctio...

Let L = d/dx +u(x) be the one-dimensional Schrödinger operator and H(x, y, t) be the corresponding heat kernel. We prove that the nth Hadamard’s coefficient Hn(x, y) is equal to 0 if and only if there exists a differential operator M of order 2n− 1 such that L = M. Thus, the heat expansion is finite if and only if the potential u(x) is a rational solution of the KdV hierarchy decaying at infini...

The weighted Cesáro operator Ch in ` (h)-spaces is investigated in terms of several concepts of normality, where h denotes a positive discrete measure on N0. We classify exactly those h for which Ch is hyponormal. Two examples related to the Haar measures of orthogonal polynomials are discussed. We show that the Cesáro operator is not always paranormal. Furthermore, we prove that the Cesáro ope...

We review an algebraic method for constructing degenerate eigenvectors of the transfer matrix of the eight-vertex Cyclic Solid-on-Solid lattice model (8V CSOS model), where the degeneracy increases exponentially with respect to the system size. We consider the elliptic quantum group Eτ,η(sl2) at the discrete coupling constants: 2Nη = m1 + im2τ , where N,m1 and m2 are integers. Then we show that...