共查询到20条相似文献,搜索用时 556 毫秒
1.
For unitary representations of the N=2 superconformal algebra, we construct a new type of resolution realized in a free-field
space with two fermionic screening operators.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2, pp. 244–257, November, 1999 相似文献
2.
Solution of the spectral problem for the curl and Stokes operators with periodic boundary conditions
R. S. Saks 《Journal of Mathematical Sciences》2006,136(2):3794-3811
In this paper, we establish relations between eigenvalues and eigenfunctions of the curl operator and Stokes operator (with
periodic boundary conditions). These relations show that the curl operator is the square root of the Stokes operator with
ν = 1. The multiplicity of the zero eigenvalue of the curl operator is infinite. The space L
2(Q, 2π) is decomposed into a direct sum of eigenspaces of the operator curl. For any complex number λ, the equation rot
u + λu = f and the Stokes equation −ν(Δv + λ 2v) + ∇p = f, div v = 0, are solved. Bibliography: 15 titles.
Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 246–276. 相似文献
3.
Mohan Joshi 《Proceedings Mathematical Sciences》1980,89(2):95-100
Let (Ω,B,μ) be ameasure space andX a separable Hubert space. LetT be a random operator from Ω ×X intoX. In this paper we investigate the measurability ofT
-1. In our main theorems we show that ifT is a separable random operator withT(w) almost sure invertible and monotone and demicontinuous thenT
-1is also a random operator. As an application of this we give an existence theorem for random Hammerstein operator equation. 相似文献
4.
I. Kh. Khusnullin 《Computational Mathematics and Mathematical Physics》2010,50(4):646-664
A perturbed two-parameter boundary value problem is considered for a second-order differential operator on an interval with
Dirichlet conditions. The perturbation is described by the potential μ−1
V((x − x
0)ɛ−1), where 0 < ɛ ≪ 1 and μ is an arbitrary parameter such that there exists δ > 0 for which ɛ/μ = o(ɛδ). It is shown that the eigenvalues of this operator converge, as ɛ → 0, to the eigenvalues of the operator with no potential.
Complete asymptotic expansions of the eigenvalues and eigenfunctions of the perturbed operator are constructed. 相似文献
5.
Maria Malejki 《Central European Journal of Mathematics》2010,8(1):114-128
We consider the problem of approximation of eigenvalues of a self-adjoint operator J defined by a Jacobi matrix in the Hilbert space l
2(ℕ) by eigenvalues of principal finite submatrices of an infinite Jacobi matrix that defines this operator. We assume the
operator J is bounded from below with compact resolvent. In our research we estimate the asymptotics (with n → ∞) of the joint error of approximation for the eigenvalues, numbered from 1 to N; of J by the eigenvalues of the finite submatrix J
n
of order n × n; where N = max{k ∈ ℕ: k ≤ rn} and r ∈ (0; 1) is arbitrary chosen. We apply this result to obtain an asymptotics for the eigenvalues of J. The method applied in this research is based on Volkmer’s results included in [23]. 相似文献
6.
Sophia Th. Kyritsi Nikolaos Matzakos Nikolaos Papageorgiou 《Czechoslovak Mathematical Journal》2005,55(3):545-579
In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a
maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator
of the form x ↦ a(x, x′)′. In this problem the maximal monotone term is required to be defined everywhere in the state space ℝN. The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ↦ (a(x)x′)′. In this case the maximal monotone term need not be defined everywhere, incorporating into our framework differential
variational inequalities. Using techniques from multivalued analysis and from nonlinear analysis, we prove the existence of
solutions for both problems under convexity and nonconvexity conditions on the multivalued right-hand side. 相似文献
7.
Toshiyuki Abe 《Mathematische Zeitschrift》2007,255(4):755-792
We give an example of an irrational C
2-cofinite vertex operator algebra whose central charge is −2d for any positive integer d. This vertex operator algebra is given as the even part of the vertex operator superalgebra generated by d pairs of symplectic fermions, and it is just the realization of the c = −2-triplet algebra given by Kausch in the case d = 1. We also classify irreducible modules for this vertex operator algebra and determine its automorphism group.
This research is supported in part by a grant from Japan Society for the Promotion of Science. 相似文献
8.
Helmut Abels 《Journal of Evolution Equations》2002,2(4):439-457
In this article we prove the existence of bounded purely imaginary powers of the Stokes operator , which is defined on the space of solenoidal vector fields < q < , where is an infinite layer. It is a consequence of a special representation of the resolvent of the Stokes operator in terms of
the Stokes operator on , a composition of a trace and a Poisson operator – a singular Green operator – and a negligible part. 相似文献
9.
M. F. Gamal’ 《Journal of Mathematical Sciences》2008,148(6):830-840
Let T be a Toeplitz operator on the Hardy space H2 on the unit circle, and let the symbol of T be of the form ϕ/ψ, where ϕ is an inner function, ψ is a finite Blaschke product,
and deg ψ ≤ deg ϕ. D. N. Clark proved that such an operator T is similar to an isometry. In this paper, we find necessary
and sufficient conditions under which such an operator T is similar to a unilateral shift. Bibliography: 20 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 85–104. 相似文献
10.
The present paper is concerned with the spectral analysis of a transport-like operator derived from a model introduced by Rotenberg describing the growth of a cell population. Each cell of this population is distinguished by its degree of maturity μ and its maturation velocity v. The biological boundaries of μ = 0 and μ = a (a > 0) are fixed and tightly coupled through mitosis. At mitosis daughter cells and mother cells are related by a general reproduction rule which covers all known biological ones. We first discuss in detail the spectrum of the streaming operator for smooth and partly smooth boundary conditions. Next, we discuss the existence and nonexistence of eigenvalues of the transport operator in the half plane {λ ∈ ℂ : Reλ > where denotes the spectral bound of the streaming operator. In particular, the strict monotonicity of the leading eigenvalue (when it exists) of the transport operator with respect to different parameters of the equation is also considered. We close the paper by describing in detail the various essential spectra of the transport operator for wide classes of collision and boundary operators. 相似文献
11.
Characterizations and Extensions of Lipschitz-α Operators 总被引:1,自引:0,他引:1
Huai Xin CAO Jian Hua ZHANG Zong Ben XU 《数学学报(英文版)》2006,22(3):671-678
In this work, we prove that a map F from a compact metric space K into a Banach space X over F is a Lipschitz-α operator if and only if for each σ in X^* the map σoF is a Lipschitz-α function on K. In the case that K = [a, b], we show that a map f from [a, b] into X is a Lipschitz-1 operator if and only if it is absolutely continuous and the map σ→ (σ o f)' is a bounded linear operator from X^* into L^∞([a, b]). When K is a compact subset of a finite interval (a, b) and 0 〈 α ≤ 1, we show that every Lipschitz-α operator f from K into X can be extended as a Lipschitz-α operator F from [a, b] into X with Lα(f) ≤ Lα(F) ≤ 3^1-α Lα(f). A similar extension theorem for a little Lipschitz-α operator is also obtained. 相似文献
12.
On positivity of solutions of degenerate boundary value problems for second-order elliptic equations
In this paper we study thedegenerate mixed boundary value problem:Pu=f in Ω,B
u
=gon Ω∂Г where ω is a domain in ℝ
n
,P is a second order linear elliptic operator with real coefficients, Γ⊆∂Ω is a relatively closed set, andB is an oblique boundary operator defined only on ∂Ω/Γ which is assumed to be a smooth part of the boundary.
The aim of this research is to establish some basic results concerning positive solutions. In particular, we study the solvability
of the above boundary value problem in the class of nonnegative functions, and properties of the generalized principal eigenvalue,
the ground state, and the Green function associated with this problem. The notion of criticality and subcriticality for this
problem is introduced, and a criticality theory for this problem is established. The analogs for the generalized Dirichlet
boundary value problem, where Γ=∂Ω, were examined intensively by many authors. 相似文献
13.
A. I. Budkin 《Siberian Mathematical Journal》2010,51(3):396-401
The dominion of a subgroup H of a group A in a quasivariety ℳ is the set of all a ∈ A with equal images under all pairs of homomorphisms from A into every group in ℳ which coincide on H. The concept of dominion provides some closure operator on the lattice of subgroups of a given group. We study the closed
subgroups with respect to this operator. We find a condition for the dominion of a divisible subgroup in quasivarieties of
metabelian groups to coincide with the subgroup. 相似文献
14.
In certain circumstances, the uncertainty, ΔS[φ], of a quantum observable, S, can be bounded from below by a finite overall constant ΔS>0, i.e., ΔS[φ]≥ΔS, for all physical states φ. For example, a finite lower bound to the resolution of distances has been used to model a natural ultraviolet cutoff at
the Planck or string scale. In general, the minimum uncertainty of an observable can depend on the expectation value, t=〈φ,S
φ〉, through a function ΔS
t
of t, i.e., ΔS[φ]≥ΔS
t
, for all physical states φ with 〈φ,S
φ〉=t. An observable whose uncertainty is finitely bounded from below is necessarily described by an operator that is merely symmetric
rather than self-adjoint on the physical domain. Nevertheless, on larger domains, the operator possesses a family of self-adjoint
extensions. Here, we prove results on the relationship between the spacing of the eigenvalues of these self-adjoint extensions
and the function ΔS
t
. We also discuss potential applications in quantum and classical information theory.
相似文献
15.
We study the asymptotic behaviour ofN(α)—the number of negative eigenvalues of the operator (-τ)
l
-αV inL
2(R
d
) for an evend and2l≥d. This is the only case where the previously known results were far from being complete. In order to describe our results
we introduce an auxiliary ordinary differential operator (system) on the semiaxis. Depending on the spectral properties of
this operator we can distinguish between three cases whereN(α) is of the Weyl-type,N(α) is of the Weyl-order but not the Weyl-type coefficient and finally whereN(α)=O(αq) withq>d/2l. 相似文献
16.
Irina Krasikova Miguel Martín Javier Merí Vladimir Mykhaylyuk Mikhail Popov 《Central European Journal of Mathematics》2009,7(4):683-693
It is known that there is a continuous linear functional on L
∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L
∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L
∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L
∞(μ) to c
0(Γ) is narrow while not every such an operator is AM-compact. 相似文献
17.
本文研究单位圆盘上Bergman型空间到Zygmund型空间上的一类推广的Volterra复合算子.利用符号函数ϕ和g刻画这类算子的有界性、紧性,并计算其本性范数. 相似文献
18.
Stefan Eilertsen 《Arkiv f?r Matematik》2000,38(1):53-75
A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (− Δ)μ inR
n
,n≥1, is obtained, for μ∈(0,1/2n)/(1,1/2n−1). This extends some results for the polyharmonic operator obtained by Maz'ya and Maz'ya-Donchev.
As in the polyharmonic case, the proof is based on a weighted positivity property of (− Δ)μ, where the weight is a fundamental solution of this operator. It is shown that this property holds for μ as above while there
is an interval [A
n
, 1/2n−A
n
], whereA
n
→1, asn→∞, with μ-values for which the property does not hold. This interval is non-empty forn≥8. 相似文献
19.
Existence of Positive Solutions for Operator Equations and Applications to Semipositone Problems 总被引:2,自引:0,他引:2
In this paper we study the existence of positive solutions of the following operator equation in a Banach space E:
where G(x, λ) = λKFx+e0, K: E↦ E is a linear completely continuous operator, F: P↦ E is a nonlinear continuous , bounded operator, e0∈ E, λ is
a parameter and P is a cone of Banach space E. Since F is not assumed to be positive and e0 may be a negative element, the operator equation is a so-called semipositone problem. We prove that under certain super-linear
conditions on the operator F the operator equation has at least one positive solution for λ > 0 sufficiently small, and that under certain sub-linear
conditions on the operator F the operator equation has at least one positive solution for λ > 0 sufficiently large. In addition, we briefly outline an application of our results which simplify previous theorems in
the literature. 相似文献
20.
Let Φ be a real valued function of one real variable, let L denote an elliptic second order formally self-adjoint differential operator with bounded measurable coefficients, and let
P stand for the Poisson operator for L. A necessary and sufficient condition on Φ ensuring the equivalence of the Dirichlet integrals of Φ ◦ Ph and P(Φ ◦ h) is obtained. We illustrate this result by some sharp inequalities for harmonic functions. Bibliography: 1 title. 相似文献