We calculate a correlation function of the Jordan-Wigner operator in a class of free-fermion models formulated on an infinite one-dimensional lattice. We represent this function in terms of the determinant of an integrable Fredholm operator, convenient for analytic and numerical investigations. By using Wick’s theorem, we avoid the form-factor summation customarily used in literature for treati...

We study on a product Banach space the properties of a class of saddle functions called partially ball weakly inf-compact. For such a function we prove that the domain of the subdifferential is nonempty, that the operator naturally associated with the subdifferential is maximal monotone, and that the subdifferential of the function is integrable. For a function in a large subclass of that class...

With increasing subsystem size and energy, bipartite entanglement entropies of energy eigenstates cross over from the groundstate scaling to a volume law. In previous work, we pointed out that, when strong or weak eigenstate thermalization (ETH) applies, all or, respectively, almost follow single crossover function. The functions are determined by entropy thermal states assume universal forms i...

in this paper, we extend and generalize some recent results on the strong laws of large numbers (slln) for pairwise independent random variables [3]. no assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). also chandra’s result on cesàro uniformly integrable r.v.’s is extended.

In this paper, we have studied the Henstock - Kurzweil integral which is a generalized Riemann means. Hen-stock natural extension of integral. We defined Banach space valued function with respect to bounded variation an real increasing function. investigated elementary properties variation. proved convergence theorems and Saks lemma functions vari-ation. Equi-integrability equi-integrable theor...

The phase space for Hamiltonians of two degrees of freedom is usually divided into stochastic and integrable components. Even when well into the stochastic regime, integrable orbits may surround small stable regions or islands. The effect of these islands on the correlation function for the stochastic trajectories is examined. Depending on the value of the parameter describing the rotation numb...

It is shown that the right-sided, left-sided, and symmetric maximal functions of any measurable function can be integrable only simultaneously. The analogous statement is proved for the ergodic maximal functions. Introduction. We deal with integrable functions on T = [0, 2π) and assume that they are extended to 2π-periodic functions on the whole line R. The class of such functions will be denot...

Bloch and Okounkov introduced an n-point correlation function on the infinite wedge space and found an elegant closed formula in terms of theta functions. This function has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc, and it can also be interpreted as correlation functions on integrable ĝl ∞ -modules of level one. Such ĝl ∞ -correlation functions at higher levels...

is completely integrable and hence L(k) is in a commuting system of differential operators with n algebraically independent operators. Then we have the following fundamental result (cf. [1]). Theorem [Heckman, Opdam]. When kα are generic, the function F (λ, k;x) has an analytic extension on R and defines a unique simultaneous eigenfunction of the commuting system of differential operators with ...

We precisely evaluate the operator norm of the uncentered Hardy-Littlewood maximal function on Lp(R1). Consequently, we compute the operator norm of the “strong” maximal function on Lp(Rn), and we observe that the operator norm of the uncentered Hardy-Littlewood maximal function over balls on Lp(Rn) grows exponentially as n → ∞. For a locally integrable function f on R, let (Mnf)(x) = sup B x 1...