排序方式: 共有13条查询结果,搜索用时 31 毫秒
1.
Andrea Posilicano 《Potential Analysis》1996,5(3):241-271
We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind
.We obtain convergence in total variation norm of the corresponding probability measures on the path space C(+;d) under hypotheses which, for example, are satisfied in the case of H
loc
1
(
d
)-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given. 相似文献
2.
Andrea Posilicano 《Mathematische Nachrichten》2014,287(16):1848-1885
Let be bounded with a smooth boundary Γ and let S be the symmetric operator in given by the minimal realization of a second order elliptic differential operator. We give a complete classification of the Markovian self‐adjoint extensions of S by providing an explicit one‐to‐one correspondence between such extensions and the class of Dirichlet forms in which are additively decomposable by the bilinear form of the Dirichlet‐to‐Neumann operator plus a Markovian form. By such a result two further equivalent classifications are provided: the first one is expressed in terms of an additive decomposition of the bilinear forms associated to the extensions, the second one uses the additive decomposition of the resolvents provided by Kre?n's formula. The Markovian part of the decomposition allows to characterize the operator domain of the corresponding extension in terms of Wentzell‐type boundary conditions. Some properties of the extensions, and of the corresponding Dirichlet forms, semigroups and heat kernels, like locality, regularity, irreducibility, recurrence, transience, ultracontractivity and Gaussian bounds are also discussed. 相似文献
3.
Antonio Giorgilli Andrea Posilicano 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1988,39(5):713-732
We consider the problem of finding a normal form for differential equations in the neighbourhood of an equilibrium point, and produce general explicit estimates for both the normal form at a finite order and the remainder, using the method of Lie transforms. With such technique, the classical Poincaré-Dulac theorems are recovered, and the problem of the stability of a reversible system of coupled harmonic oscillators up to exponentially large times is discussed.
Riassunto Si considera il problema di porre in forma normale un sistema di equazioni differenziali nell'intomo di un punto di equilibrio, e si danno in generale stime esplicite sia per la forma normale troncata ad un ordine finito che per i resti. Si fa uso dell'algoritmo della trasformata di Lie. Con questo metodo si riottengono i teoremi classici di Poincaré-Dulac, e si discute il problema della stabilità per tempi esponenzialmente lunghi di un sistema reversibile di oscillatori armonici accoppiati.相似文献
4.
Finite speed of propagation and local boundary conditions for wave equations with point interactions
Pavel Kurasov Andrea Posilicano 《Proceedings of the American Mathematical Society》2005,133(10):3071-3078
We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of propagation.
5.
We investigate one-dimensional (2p × 2p)-matrix Dirac operators DX,α and DX,β with point matrix interactions on a discrete set X. Several results of [4] are generalized to the case of (p × p)-matrix interactions with p > 1. It is shown that a number of properties of the operators DX,α and DX,β (self-adjointness, discreteness of the spectrum, etc.) are identical to the corresponding properties of some Jacobi matrices BX,α and BX,β with (p × p)-matrix entries. The relationship found is used to describe these properties as well as conditions of continuity and absolute continuity of the spectra of the operators DX,α and DX,β. Also the non-relativistic limit at the velocity of light c → ∞ is studied. 相似文献
6.
We give a complete characterization, including a Lévy–Itô decomposition, of Poincaré-invariant Markov processes on
, the relativistic phase space in 1+1 spacetime dimensions. Then, by means of such processes, we construct Poincaré-invariant Gaussian random fields, and we prove a no-go theorem for the random fields corresponding to Brownian motions on
. 相似文献
7.
V.?BudyikaEmail author M.?Malamud A.?Posilicano 《Russian Journal of Mathematical Physics》2017,24(4):426-435
We consider two families of realizations of the 2p×2p–Dirac differential expression with point interactions on a discrete set X = {x n }n=1∞ ? ? on a half–line (line) and generalize certain results from [10] to the matrix case. We show that these realizations are always self-adjoint. We investigate the nonrelativistic limit as the velocity of light tends to infinity. 相似文献
8.
Gianfausto Dell'Antonio Andrea Posilicano 《Communications in Mathematical Physics》1991,141(3):559-576
Let t,
t
n
,n1, be solutions of Schrödinger equations with potentials form-bounded by –1/2 and initial data inH
1(
d
). LetP, P
n
,n1, be the probability measures on the path space =C(+,
d
) given by the corresponding Nelson diffusions. We show that if {
t
n
}
n1 converges to t inH
1(
d
), uniformly int over compact intervals, then converges to in total variation t0. Moreover, if the potentials are in the Kato classK
d
, we show that the above result follows fromH
1-convergence of initial data, andK
d
-convergence of potentials. 相似文献
9.
10.
Andrea Posilicano 《Journal of Functional Analysis》2005,223(2):259-310
Given, on the Hilbert space H0, the self-adjoint operator B and the skew-adjoint operators C1 and C2, we consider, on the Hilbert space H?D(B)⊕H0, the skew-adjoint operator