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Allal Ghanmi Youssef Hantout Ahmed Intissar Changgui Zhang Azzouz Zinoun 《The Ramanujan Journal》2008,16(3):271-284
In this paper, we introduce a notion of similarly self dual lattice in a d-dimensional Euclidean space and a classical Jacobi theta function is associated to such a lattice. We establish identities
of arithmetic type between values of this theta function and its successive derivatives. This work can be related to the spectral
theory of the Landau operators.
相似文献
3.
We provide two kinds of representations for the Taylor coefficients of the Weierstrass σ-function σ(?;Γ) associated to an arbitrary lattice Γ in the complex plane \(\mathbb{C}=\mathbb{R}^{2}\) , the first one in terms of the so-called Hermite–Gauss series over Γ and the second one in terms of Hermite–Gauss integrals over \(\mathbb{C}\) . 相似文献
4.
K. Gasmi S. Skowronek A. González Ureña 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2005,33(3):399-403
The laser-induced intracluster Ba..FCH3+ hν →
Ba* + CH3F photofragmentation has been investigated in the
13158–13736 cm-1 energy range, corresponding to the electronic
Ã′-state of the Ba..FCH3 molecule. The major photofragmentation
path was found to be the non-reactive Ba* + CH3F channel.
The photodepletion action spectrum of the Ba..FCH3 was measured
using nanosecond pump and probe technique, showing a broad feature with
a maximum photodepletion cross-section of 8 Å2. The action
spectrum of the non-reactive Ba photofragmentation channel was also
measured. The results are discussed in the light of a proposed mechanism
for the harpooning reaction leading to BaF when the complex is excited to
the à electronic state. 相似文献
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Abdelkader Intissar 《Journal of Mathematical Analysis and Applications》2005,305(2):669-689
The Reggeon field theory is governed by a non-self adjoint operator constructed as a polynomial in A, A*, the standard Bose annihilation and creation operators. In zero transverse dimension, this Hamiltonian acting in Bargmann space is defined by
Hλ′,μ=λ′A*2A2+μA*A+iλA*(A*+A)A, 相似文献
7.
The main purpose of this article is to study the L
p
-boundedness of linear and bilinear multiplier operators for the Dunkl transform in the one dimensional case. 相似文献
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The Ramanujan Journal - We investigate some basic analytic properties of the $$L^2$$ -holomorphic automorphic functions on a g-complex vector space associated with isotropic discrete subgroups... 相似文献
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Marie Thérèse Aimar Abdelkader Intissar Jean Martin Paoli 《Communications in Mathematical Physics》1993,156(1):169-177
We consider a closed densely defined linear operatorT in a Hilbert spaceE, and assume the existence of
0 (T) such thatK = (T -
0
I)-1 is compact and the existence ofp>0 such thats
n
(K)=o((n
–1/p)), whereS
n
(K) denotes the sequence of non-zero eigenvalues of the compact hermitian operator
. In this work, sufficient conditions (announced in [1]) are introduced to assure that the closed subspace ofE spanned by the generalized eigenvectors ofT coincides withE. These conditions are in particular verified by a family of non-self-adjoint operators arising in reggeon's field theory. 相似文献
10.
Abdelkader Intissar 《Communications in Mathematical Physics》1987,113(2):263-297
In this paper, we study a few spectral properties of a non-symmetrical operator arising in the Gribov theory. The first and second section are devoted to Bargmann's representation and the study of general spectral properties of the operator: $$\begin{gathered} H_{\lambda ',\mu ,\lambda ,\alpha } = \lambda '\sum\limits_{j = 1}^N {A_j^{ * 2} A_j^2 + \mu \sum\limits_{j = 1}^N {A_j^ * A_j + i\lambda \sum\limits_{j = 1}^N {A_j^ * (A_j + A_j^ * )A_j } } } \hfill \\ + \alpha \sum\limits_{j = 1}^{N - 1} {(A_{j + 1}^ * A_j + A_j^ * A_{j + 1} ),} \hfill \\ \end{gathered}$$ whereA* j andA j ,j∈[1,N] are the creation and annihilation operators. In the third section, we restrict our study to the case of nul transverse dimension (N=1). Following the study done in [1], we consider the operator: $$H_{\lambda ',\mu ,\lambda } = \lambda 'A^{ * 2} A^2 + \mu A^ * A + i\lambda A^ * (A + A^ * )A,$$ whereA* andA are the creation and annihilation operators. For λ′>0 and λ′2≦μλ′+λ2. We prove that the solutions of the equationu′(t)+H λ′, μ,λ u(t)=0 are expandable in series of the eigenvectors ofH λ′,μ,λ fort>0. In the last section, we show that the smallest eigenvalue σ(α) of the operatorH λ′,μ,λ,α is analytic in α, and thus admits an expansion: σ(α)=σ0+ασ1+α2σ2+..., where σ0 is the smallest eigenvalue of the operatorH λ′,μ,λ,0. 相似文献