相关论文: Exponential Operators, Dobinski Relations and Summ…

We study infinite order differential operators acting in the spaces of exponential type entire functions. We derive conditions under which such operators preserve the set of Laguerre entire functions which consists of the polynomials…

We consider the k-th order statistic from unit exponential distribution and show that it can be represented as a sum of independent exponential random variables. Our proof is simple and different. It readily proves that the standardized…

For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach…

The conversion of resolvent conditions into semigroup estimates is crucial in the stability analysis of hyperbolic partial differential equations. For two families of multiple Toeplitz operators, we relate the power bound with a resolvent…

Moving beyond the classical additive and multiplicative approaches, we present an "exponential" method for perturbative renormalization. Using Dyson's identity for Green's functions as well as the link between the Faa di Bruno Hopf algebra…

Volume polynomials measure the growth of Minkowski sums of convex bodies and of tensor powers of positive line bundles on projective varieties. We show that Aluffi's covolume polynomials are precisely the polynomial differential operators…

It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I…

Summation methods play a very important role in quantum field theory because all perturbation series are divergent and the expansion parameter is not always small. A number of methods have been tried in this context, most notably Pade…

An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials, gives the possibility to associate to any numerical…

We use a new $q$-exponential operator based on the $q^{\pm1}$-derivative $\D_{q^{\pm1}}$ of order 1 to derive summation formulas for bilateral basic hypergeometric series ${}_{0}\psi_{1}$, ${}_{1}\psi_{1}$, ${}_{1}\psi_{2}$, and…

q- Dobinski formula may be interpreted as the average of powers of a random variable X_q with the q- Poisson distribution.

We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…

The exponential cubic B-spline functions are used to set up the collocation method for finding solutions of the Burgers's equation. The effect of the exponential cubic B-splines in the collocation method is sought by studying four text…

Let $L$ be a linear differential operator with constant coefficients of order $n$ and complex eigenvalues $\lambda_{0},...,\lambda_{n}$. Assume that the set $U_{n}$ of all solutions of the equation $Lf=0$ is closed under complex…

We propose a new boson expansion method using a norm operator. The small parameter expansion, in which the boson approximation becomes the zeroth-order approximation, requires the double commutation relations between phonon operators that…

I recently proposed a method of bosonization valid for systems of an even number of fermions whose partition function is dominated at low energy by bosonic composites. This method respects all symmetries, in particular fermion number…

The robustness property of exponential dichotomies refers to the stability of this notion under small linear perturbations. In recent work~\cite{PPX}, the authors have identified a new class of perturbations under which the notion of a…

There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…

The Heisenberg Oscillator Algebra admits irreducible representations both on the ring $B$ of polynomials in infinitely many indeterminates (the {\em bosonic representation}) and on a graded-by-{\em charge} vector space, the {\em…

We derive and discuss a technique for manipulating power series which is complementary to standard procedures. We begin with the translation operator, but we express the operator as an infinite product instead of expanding it as a series…