The Gamma kernel is a projection kernel of the form (A(x)B(y) − B(x)A(y))/(x − y), where A and B are certain functions on the one-dimensional lattice expressed through Euler’s Γfunction. The Gamma kernel depends on two continuous parameters; its principal minors serve as the correlation functions of a determinantal probability measure P defined on the space of infinite point configurations on t...

Quantum trajectories are Markov processes that describe the time evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they defined as solutions so-called Stochastic Schrödinger Equations, which nonlinear stochastic differential equations driven by Poisson and Wiener processes. This paper is devoted to study invariant measures trajectories. Particularly, we p...

We exhibit a change of variables that maintains the Mahler measure given polynomial. This method leads to construction highly non-trivial polynomials with and settles some conjectural numerical formulas due Boyd Brunault.

g. darbo [rend. sem. math. univ. padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. in this paper, we apply the darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.

Abstract Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as counterpart Bowen entropy. In present paper we give systematic study for continuous G -action system $(X,G)$ , where X compact metric space and countable infinite discrete amenable group. We first prove variational principle entropy: any Borel subset Z equals supremum upper local over al...