共查询到20条相似文献,搜索用时 15 毫秒
1.
Olaf Post 《Annales Henri Poincare》2006,7(5):933-973
We consider a family of non-compact manifolds Xε (“graph-like manifolds”) approaching a metric graph X0 and establish convergence results of the related natural operators, namely the (Neumann) Laplacian
and the generalized Neumann (Kirchhoff) Laplacian
on the metric graph. In particular, we show the norm convergence of the resolvents, spectral projections and eigenfunctions.
As a consequence, the essential and the discrete spectrum converge as well. Neither the manifolds nor the metric graph need
to be compact, we only need some natural uniformity assumptions. We provide examples of manifolds having spectral gaps in
the essential spectrum, discrete eigenvalues in the gaps or even manifolds approaching a fractal spectrum. The convergence
results will be given in a completely abstract setting dealing with operators acting in different spaces, applicable also
in other geometric situations.
Communicated by Claude Alain Pillet
Submitted: December 21, 2005 Accepted: January 30, 2006 相似文献
2.
Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions,i.e.,null solutions to a first order vector valued rotation invariant differential operator (θ) ca... 相似文献
3.
We introduce the notion of strong supercommutativity of self-adjoint operators on a
-graded Hilbert space and give some basic properties. We clarify that strong supercommutativity is a unification of strong commutativity and strong anticommutativity. We also establish the theory of super quantization. Applications to supersymmetric quantum field theory and a fermion-boson interaction system are discussed. 相似文献
4.
We exhibit a vertex operator that implements the multiplication by power sums of Jucys–Murphy elements in the centers of the group algebras of all symmetric groups simultaneously. The coefficients of this operator generate a representation of
, to which operators multiplying by normalized conjugacy classes are also shown to belong. A new derivation of such operators based on matrix integrals is proposed, and our vertex operator is used to give an alternative approach to the polynomial functions on Young diagrams introduced by Kerov and Olshanski. Bibliography: 18 titles. 相似文献
5.
We consider the heat operator of a Bismut superconnection for a family of generalized Dirac operators defined along the leaves of a foliation with Hausdorff graph. We assume that the strong Novikov–Shubin invariants of the Dirac operators are greater than three times the codimension of the foliation. We compute the t asymptotics associated to a rescaling of the metric by 1/t and show that the heat operator converges to the Chern character of the index bundle of the operator. Combined with previous results, this gives a general families index theorem for such operators. 相似文献
6.
David Eelbode 《Advances in Applied Clifford Algebras》2007,17(4):635-649
We introduce a framework for studying differential operators which are invariant with respect to the real (complex) symplectic
Lie algebra
(
), associated to a quaternionic structure on a vector space
. To do so, these algebras are realized within the orthogonal Lie algebra
. This leads in a natural way to a refinement of the recently introduced notion of complex Hermitean Clifford analysis, in
which four variations of the classical Dirac operator play a dominant role.
David Eelbode: Postdoctoral fellow supported by the F.W.O. Vlaanderen (Belgium). 相似文献
7.
We introduce two new linear differential operators which are invariant with respect to the unitary group SU(n). They constitute analogues of the twistor and the Rarita-Schwinger operator in the orthogonal case. The natural setting for doing this is Hermitian Clifford Analysis. Such operators are constructed by twisting the two versions of the Hermitian Dirac operator 6z_ and 6z_ and then projecting on irreducible modules for the unitary group. We then study some properties of their spaces of nullsolutions and we find a formulation of the Hermitian Rarita-Schwinger operators in terms of Hermitian monogenic polynomials. 相似文献
8.
Let (X, ~) be a combinatorial graph the vertex set X of which is a discrete metric space. We suppose that a discrete group G acts freely on (X, ~) and that the fundamental domain with respect to the action of G contains only a finite set of points. A graph with these properties is called periodic with respect to the group G. We examine the Fredholm property and the essential spectrum of band-dominated operators acting on the spaces l
p
(X) or c_0(X), where (X, ~) is a periodic graph. Our approach is based on the thorough use of band-dominated operators. It generalizes the necessary
and sufficient results obtained in [39] in the special case and in [42] in case X = G is a general finitely generated discrete group.
Submitted: May 21, 2007. Revised: September 25, 2007. Accepted: November 5, 2007. 相似文献
9.
We examine the operator algebra
behind the boundary integral equation method for solving transmission problems. A new type of boundary integral operator, the rotation operator, is introduced, which is more appropriate than operators of double layer type for solving transmission problems for first order elliptic partial differential equations. We give a general invertibility criteria for operators in
by defining a Clifford algebra valued Gelfand transform on
. The general theory is applied to transmission problems with strongly Lipschitz interfaces for the two classical elliptic operators
and . We here use Rellich techniques in a new way to estimate the full complex spectrum of the boundary integral operators. For
we use the associated rotation operator to solve the Hilbert boundary value problem and a Riemann type transmission problem. For the Helmholtz equation, we demonstrate how Rellich estimates give an angular spectral estimate on the rotation operator, which with the general spectral mapping properties in
translates to a hyperbolic spectral estimate for the double layer potential operator. 相似文献
10.
Lukáš Krump 《Advances in Applied Clifford Algebras》2009,19(2):365-374
The Dirac operator in several operators is an analogue of the - operator in theory of several complex variables. The Hartog’s type phenomena are encoded in a complex of invariant differential
operators starting with the Dirac operator, which is an analogue of the Dolbeault complex. In the paper, a construction of
the complex is given for the Dirac operator in 4 variables in dimension 6 (i.e. in the non-stable range). A peculiar feature
of the complex is that it contains a third order operator. The methods used in the construction are based on the Penrose transform
developed by R. Baston and M. Eastwood.
The work presented here is a part of the research project MSM 0021620839 and was supported also by the grant GA ČR 201/05/2117. 相似文献
11.
12.
F. Brackx H. De Schepper N. De Schepper F. Sommen 《Advances in Applied Clifford Algebras》2007,17(3):311-330
Orthogonal Clifford analysis in flat m–dimensional Euclidean space focusses on monogenic functions, i.e. null solutions of the rotation invariant vector valued
Dirac operator
, where (
) forms an orthogonal basis for the quadratic space
underlying the construction of the Clifford algebra
. When allowing for complex constants and taking the dimension to be even: m = 2n, the same set of generators produces the complex Clifford algebra
, which we equip with a Hermitean Clifford conjugation and a Hermitean inner product. Hermitean Clifford analysis then focusses
on the simultaneous null solutions of two mutually conjugate Hermitean Dirac operators, naturally arising in the present context
and being invariant under the action of a realization of the unitary group U (n). In this so–called Hermitean setting Clifford–Hermite polynomials are constructed, starting from a Rodrigues formula involving
both Dirac operators mentioned. Due to the specific features of the Hermitean setting, four different types of polynomials
are obtained, two types of even degree and two types of odd degree. We investigate their properties: recurrence relations,
structure, explicit form and orthogonality w.r.t. a deliberately chosen weight function. They also give rise to the definition
of the Hermitean Clifford–Hermite functions, and may be used to develop a Hermitean continuous wavelet transform, see [4]. 相似文献
13.
14.
For an arbitrary class of graphs , there may not exist a function f such that , for every . When such a function exists, it is called a χ-binding function for . The problem of finding an optimal χ-binding function for the class of 3K
1-free graphs is open. In this paper, we obtain linear χ-binding function for the class of {3K
1, H}-free graphs, where H is one of the following graphs: , House graph and Kite graph. We first describe structures of these graphs and then derive χ-binding functions. 相似文献
15.
Hermitean Clifford analysis is a recent branch of Clifford analysis, refining the Euclidean case; it focusses on the simultaneous
null solutions, called Hermitean monogenic functions, of two complex Dirac operators which are invariant under the action
of the unitary group. The specificity of the framework, introduced by means of a complex structure creating a Hermitean space,
forces the underlying vector space to be even dimensional. Thus, any Hilbert convolution kernel in should originate from the non-tangential boundary limits of a corresponding Cauchy kernel in . In this paper we show that the difficulties posed by this inevitable dimensional jump can be overcome by following a matrix
approach. The resulting matrix Hermitean Hilbert transform also gives rise, through composition with the matrix Dirac operator,
to a Hermitean Hilbert–Dirac convolution operator “factorizing” the Laplacian and being closely related to Riesz potentials.
Received: October, 2007. Accepted: February, 2008. 相似文献
16.
17.
O. Aichholzer G. Araujo-Pardo N. García-Colín T. Hackl D. Lara C. Rubio-Montiel J. Urrutia 《Graphs and Combinatorics》2016,32(2):431-451
The pseudoachromatic index of a graph is the maximum number of colors that can be assigned to its edges, such that each pair of different colors is incident to a common vertex. If for each vertex its incident edges have different color, then this maximum is known as achromatic index. Both indices have been widely studied. A geometric graph is a graph drawn in the plane such that its vertices are points in general position, and its edges are straight-line segments. In this paper we extend the notion of pseudoachromatic and achromatic indices for geometric graphs, and present results for complete geometric graphs. In particular, we show that for n points in convex position the achromatic index and the pseudoachromatic index of the complete geometric graph are \(\lfloor \frac{n^2+n}{4} \rfloor \). 相似文献
18.
Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifolds, fractals, graphs etc.). Boundedness on L p for pseudodifferential operators of order 0 is proved. We mainly focus on symbols belonging to the class $S^{0}_{1,\delta}$ for δ∈[0,1). For the limit class $S^{0}_{1,1}$ , we describe some results by restricting our attention to the case of a sub-Laplacian operator on a Riemannian manifold. 相似文献
19.
Elena Cordero Stevan Pilipović Luigi Rodino Nenad Teofanov 《Mediterranean Journal of Mathematics》2005,2(4):381-394
We study localization operators within the framework of ultradistributions. More precisely, given a symbol a and two windows φ1, φ2, we investigate the multilinear mapping from
to the localization operator
Results are formulated in terms of modulation spaces with weights which may have exponential growth. We give sufficient and
necessary conditions for
a to be bounded or to belong to a Schatten class. As an application, we study symbols defined by ultra-distributions with
compact support, that give trace class localization operators. 相似文献
20.
We consider the =2 supersymmetric massive Yang-Mills field theory formulated in the =2 harmonic superspace. We present various gauge-invariant forms of writing the mass term in the action (in particular, using
the Stueckelberg superfield), which result in dual formulations of the theory. We develop a gaugeinvariant and explicitly
supersymmetric scheme of the loop expansion of the superfield effective action beyond the mass shell. In the framework of
this scheme, we calculate gauge-invariant and explicitly =2 supersymmetric one-loop counterterms including new counterterms depending on the Stueckelberg superfield. We analyze the
component structure of one of these counterterms.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 22–40, October, 2008. 相似文献