asymptotic completeness for n body stark hamiltonians we prove asymptotic completeness for short and long rangen body stark hamiltonians with local singularities of at most coulomb type our results include the usual models for atoms and molecules

gamow vectors and borel summability in a class of quantum systems we analyze the detailed time dependence of the wave function x t for one dimensional hamiltonians h partial x 2 v x where v for example modeling barriers or wells and x 0 are compactly supported

spectral theory for 1 body stark operators abstract we investigate spectral theory for a one body stark hamiltonian under minimum regularity and decay conditions on the potential actually allowing sub linear growth at infinity our results include rellich s theorem the limiting absorption principle radiation condition bounds and sommerfeld s uniqueness and most of these are stated and proved in sharp form employing besov type spaces for the proofs we adopt a commutator scheme by ito skibsted 13 a feature of the paper is a special choice of an escape function related to parabolic coordinates which conforms well with classical mechanics for the stark hamiltonian the whole setting of the paper such as the conjugate operator and the besov type spaces is generated by this single escape function we apply our results in the sequel paper 5

a determinantal approach to appell polynomials a new definition by means of a determinantal form for appell 1880 1 polynomials is given general properties some of them new are proved by using elementary linear algebra tools finally classic and non classic examples are considered and the coefficients calculated by an ad hoc mathematica code for particular sequences of appell polynomials are given

recurrence relations for polynomial sequences via riordan matrices we give recurrence relations for any family of generalized appell polynomials unifying so some known recurrences for many classical sequences of polynomials our main tool to get our goal is the riordan group we use the product of riordan matrices to interpret some relationships between different polynomial families moreover using the hadamard product of series we get a general recurrence relation for the polynomial sequences associated to the so called generalized umbral calculus

ionization of coulomb systems in mathbb r 3 by time periodic forcings of arbitrary size we analyze the long time behavior of solutions of the schrodinger equation i psi t delta b r v t x psi x in mathbb r 3 r x describing a coulomb system subjected to a spatially compactly supported time periodic potential v t x v t 2 x with zero time average

asymptotic completeness for n body short range quantum systems a new proof we give an alternative geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through shortrange pair potentials it relies on an estimate showing that the intercluster motion concentrates asymptotically on classical trajectories

riordan arrays and related polynomial sequences abstract in this paper we generalize the results due to luzon and moron and present a characterization of the generalized riordan arrays using this characterization we establish a recurrence for the generalized sheffer sequences and study some special types of polynomial sequences including the generalized lucas u sequence and v sequence and the generalized humbert polynomial sequence in particular by appealing to the factorizations of riordan arrays the umbral composition of polynomial sequences and the hadamard product of series we establish various relations among these polynomial sequences thus we give a unified approach to some well known polynomial sequences appeared in combinatorics and the theory of special functions

propagation estimates for n body schroedinger operators we prove propagation estimates of strong type for long rangen body hamiltonians emphasis is on phase space analysis in the free channel region

the n particle scattering problem asymptotic completeness for short range systems on demontre la completude asymptotique pour des systemes de mecanique quantique a courte portee constitues d un nombre arbitraire de particules

exponential bounds and absence of positive eigenvalues for n body schrodinger operators for a large class ofn body potentialsv we prove that if is an eigenfunction of v with eigenvaluee then sup 2 e 0 exp x l2 is either a threshold or consequences of this result are the absence of positive eigenvalues and optimal l2 exponential lower bounds

a determinantal approach to sheffer sequences abstract in this paper by using the theory of riordan arrays and the relations between sheffer sequences and riordan arrays we give a determinantal definition for sheffer sequences based on this new definition some general properties of sheffer sequences are reproved and the determinantal representations of some well known sheffer sequences are presented

bijections and the riordan group one of the cornerstone ideas in mathematics is to take a problem and to look at it in a bigger space in this paper we examine combinatorial sequences in the context of the riordan group various subgroups of the riordan group each give us a different view of the original sequence in many cases this leads to both a combinatorial interpretation and to eco rewriting rules in this paper we will concentrate on just four of the subgroups of the riordan group to demonstrate some of the possibilities of this approach

asymptotic completeness for n body quantum systems with long range interactions in a time periodic electric field we show the asymptotic completeness for n body quantum systems with long range interactions in a time periodic electric field whose mean in time is non zero where n 2 one of the main ingredients of this paper is to give some propagation estimates for physical propagators generated by time periodic hamiltonians which govern the systems under consideration

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

asymptotic completeness of long range n body quantum systems where x is a euclidean space and lra a e a is a finite family of projections onto certain subspaces xa of x we will always assume that the family xa a e a is closed with respect to the algebraic sum and contains xamin 0 the class of operators of the form 0 2 is a generalization of 0 1 up to a linear change of coordinates in the configuration space x they usually go under the name of generalized n body schrbdinger operators and were first considered in a in what follows we will drop the word generalized we refer the reader to rsi vol iii for a general introduction to n body schr6dinger operators defined as in equation 0 1 we will consistently use the definition 0 2 and assume that the reader is familiar with the physical meaning of various objects under study

criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed stark type operators abstract in this paper we consider the perturbed stark operator h u h 0 u q u u x u q u where q is the power decaying perturbation the criteria for q such that h h 0 q has at most one eigenvalue finitely many infinitely many eigenvalues are obtained all the results are quantitative and are generalized to the perturbed stark type operator

cayley continuants in 1858 cayley considered a particular kind of tridiagonal determinants or continuants by a direct inspection of the first cases he conjectured an identity expressing these determinants in terms of certain other determinants considered by sylvester in 1854 then cayley proved the conjectured identity by induction but as he wrote he felt unsatisfied with his proof the main aim of this paper is to give a straightforward proof of cayley s identity using the method of formal series moreover we use this method and umbral calculus techniques to obtain several other identities cayley continuants appear in several contexts and in particular in enumerative combinatorics mittag leffler polynomials meixner polynomials of the first kind the falling and the raising factorials are just few instances of these continuants they can be interpreted in terms of weighted permutations moreover as we prove in this paper they also appear in the context of hankel determinants generated by certain catalan like numbers

recurrence relations for the sheffer sequences abstract in this paper using the production matrix of an exponential riordan array g t f t we give a recurrence relation for the sheffer sequence for the ordered pair g t f t we also develop a new determinant representation for the general term of the sheffer sequence as applications determinant expressions for some classical sheffer polynomial sequences are derived

spectral analysis of n body stark hamiltonians we prove that the spectrum for a large class ofn body stark hamiltonians is purely absolutely continuous we need slow decay at infinity and local singularities of at most coulomb type in particular our results include the usual models for atoms and molecules