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1.
We classify all bundle functors G admitting natural operators transforming connections on a fibered manifold Y → M into connections on GY → M. Then we solve a similar problem for natural operators transforming connections on Y → M into connections on GY → Y.
Dedicated to Professor Ivan Kolář on the occasion of his 70th birthday 相似文献
2.
We determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal
bundle with structure group O(n), SO(n) or Sp(n) over a closed, simply connected manifold of dimension 4. On the way we derive a classification of Howe subgroups of SO(n) up to conjugacy. 相似文献
3.
On conformal manifolds of even dimension n ≥ 4 we construct a family of new conformally invariant differential complexes, each containing one coboundary operator of order greater than 1. Each bundle in each of these complexes appears either in the de Rham complex or in its dual (which is a different complex in the non-orientable case). Each of the new complexes is elliptic in case the conformal structure has Riemannian signature. We also construct gauge companion operators which (for differential forms of order k ≤ n/2) complete the exterior derivative to a conformally invariant and (in the case of Riemannian signature) elliptically coercive system. These (operator, gauge) pairs are used to define finite dimensional conformally stable form subspaces which are are candidates for spaces of conformal harmonics. This generalizes the n/2-form and 0-form cases, in which the harmonics are given by conformally invariant systems. These constructions are based on a family of operators on closed forms which generalize in a natural way Branson's Q-curvature. We give a universal construction of these new operators and show that they yield new conformally invariant global pairings between differential form bundles. Finally we give a geometric construction of a family of conformally invariant differential operators between density-valued differential form bundles and develop their properties (including their ellipticity type in the case of definite conformal signature). The construction is based on the ambient metric of Fefferman and Graham, and its relationship to the tractor bundles for the Cartan normal conformal connection. For each form order, our derivation yields an operator of every even order in odd dimensions, and even order operators up to order n in even dimension n. In the case of unweighted (or true) forms as domain, these operators are the natural form analogues of the critical order conformal Laplacian of Graham et al., and are key ingredients in the new differential complexes mentioned above. 相似文献
4.
Josef Janyška 《Central European Journal of Mathematics》2005,3(2):294-308
We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent
bundle of a manifold with a linear (non-symmetric) connection.
This paper has been supported by the Grant Agency of the Czech Republic under the Project number GA 201/02/0225. 相似文献
5.
6.
Ulrich Bunke 《Mathematische Nachrichten》1994,165(1):191-203
We consider families of generalized Dirac operators Dt with constant principal symbol and constant essential spectrum such that the endpoints are gauge equivalent, i.e., D1 = W*D0W. The spectral flow un any gap in the essential spectrum we express as the Fredholm index of 1 + (W - 1)P where P is the spectral projection on the interval d, ∞) with respect to D0 and d is in the gap. We reduce the computation of this index to the Atiyah-Singer index theorem for elliptic pseudodifferential operators. We find an invariant of the Riemannian geometry for odd dimensional spin manifolds estimating the length of gaps in the spectrum of the Dirac operator. 相似文献
7.
We outline the proof of a theorem of Vafa-Witten type on uniform bounds for the eigenvalues of a family of transversal Dirac
operators relative to a Riemannian foliation. The family in question is parameterized by a moduli space of basic connections
with respect to the foliation modulo a suitable group of foliation preserving gauge transformations. The proof is based on
the concept of spectral flow, applied to the suspension of suitable gauge transformations to periodic families of Dirac operators.
Work supported in part by a grant from the National Science Foundation. 相似文献
8.
A real square matrix A is called a P-matrix if all its principal minors are positive. Such a matrix can be characterized by the sign non-reversal property. Taking a cue from this, the notion of a P-operator is extended to infinite dimensional spaces as the first objective. Relationships between invertibility of some subsets of intervals of operators and certain P-operators are then established. These generalize the corresponding results in the matrix case. The inheritance of the property of a P-operator by the Schur complement and the principal pivot transform is also proved. If A is an invertible M-matrix, then there is a positive vector whose image under A is also positive. As the second goal, this and another result on intervals of M-matrices are generalized to operators over Banach spaces. Towards the third objective, the concept of a Q-operator is proposed, generalizing the well known Q-matrix property. An important result, which establishes connections between Q-operators and invertible M-operators, is proved for Hilbert space operators. 相似文献
9.
In the short-string limit, we present results for the one-loop correction to the energy of string solutions in AdS
5
× S
5
that belong to a certain class. The computations are based on the observation that the fluctuation operators, just as for
rigid spinning-string elliptic solutions, can be written in the single-gap Lamé form. Based on these computations, we reveal
a remarkable universality of the expression for the energy of short semiclassical strings, which may help in better understanding
the structure of the strongcoupling expansion of the anomalous dimensions of dual gauge theory operators. 相似文献
10.
In this paper we prove a well-posedness result for the Cauchy problem. We study a class of first order hyperbolic differential
[2] operators of rank zero on an involutive submanifold ofT
*
R
n+1-{0} and prove that under suitable assumptions on the symmetrizability of the lifting of the principal symbol to a natural
blow up of the “singular part” of the characteristic set, the operator is strongly hyperbolic. 相似文献
11.
We review a variety of recently obtained trace formulae for (multidimensional) Schrödinger operators and indicate their connections with the KdV hierarchy in one dimension. Our principal new result in this paper concerns a set of trace formulae in 1 d 3 dimensions related to point interactions. 相似文献
12.
Abdurahman Masoud Abdalla 《Quaestiones Mathematicae》2018,41(4):529-539
This paper deals with an order-theoretic analysis of certain structures studied in category theory. A categorical closure operator (cco in short) is a structure on a category, which mimics the structure on the category of topological spaces formed by closing subspaces of topological spaces. Such structures play a significant role not only in categorical topology, but also in topos theory and categorical algebra. In the case when the category is a poset, as a particular instance of the notion of a cco, one obtains what we call in this paper a binary closure operator (bco in short). We show in this paper that bco’s allow one to see more easily the connections between standard conditions on general cco’s, and furthermore, we show that these connections for cco’s can be even deduced from the corresponding ones for bco’s, when considering cco’s relative to a well-behaved class of monorphisms as in the literature. The main advantage of the approach to such cco’s via bco’s is that the notion of a bco is self-dual (relative to the usual posetal duality), and by applying this duality to cco’s, independent results on cco’s are brought together. In particular, we can unify basic facts about hereditary closure operators with similar facts about minimal closure operators. Bco’s also reveal some new links between categorical closure operators, the usual unary closure and interior operators, modularity law in order and lattice theory, the theory of factorization systems and torsion theory. 相似文献
13.
14.
Heikki Orelma 《Advances in Applied Clifford Algebras》2012,22(1):143-158
In this paper we express the theory of harmonic differential forms on conformal Euclidean manifolds in terms of the so called
Clifford multivector fields. The aim is to give good definitions for d and d* operators in Clifford multivector case. Using these definitions we derive a formula for the Laplace operator. Three fundamental
examples are included in the end of the paper and connections to existing theory is discussed. 相似文献
15.
Ivan Kolář 《Central European Journal of Mathematics》2003,1(3):360-366
For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher
order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches. 相似文献
16.
J. J. Betancor A. J. Castro J. Curbelo 《Journal of Fourier Analysis and Applications》2011,17(5):932-975
In this paper we prove L
p
-boundedness properties of spectral multipliers associated with multidimensional Bessel operators. In order to do this we
estimate the L
p
-norm of the imaginary powers of Bessel operators. We also prove that the Hankel multipliers of Laplace transform type on
(0,∞)
n
are principal value integral operators of weak type (1,1). 相似文献
17.
A.F.M. ter Elst Derek W. Robinson 《Calculus of Variations and Partial Differential Equations》1999,8(4):327-363
Let G be a connected Lie group with Lie algebra and an algebraic basis of . Further let denote the generators of left translations, acting on the -spaces formed with left Haar measure dg, in the directions . We consider second-order operators corresponding to a quadratic form with complex coefficients , , , . The principal coefficients are assumed to be H?lder continuous and the matrix is assumed to satisfy the (sub)ellipticity condition uniformly over G. We discuss the hierarchy relating smoothness properties of the coefficients of H with smoothness of the kernel. Moreover, we establish Gaussian type bounds for the kernel and its derivatives. Similar theorems
are proved for operators in nondivergence form for which the principal coefficients are at least once differentiable.
Received January 24, 1997 / Accepted June 5, 1998 相似文献
18.
Wen-Chi Kuo 《Journal of Mathematical Analysis and Applications》2005,303(2):509-521
Conditional expectations operators acting on Riesz spaces are shown to commute with a class of principal band projections. Using the above commutation property, conditional expectation operators on Riesz spaces are shown to be averaging operators. Here the theory of f-algebras is used when defining multiplication on the Riesz spaces. This leads to the extension of these conditional expectation operators to their so-called natural domains, i.e., maximal domains for which the operators are both averaging operators and conditional expectations. The natural domain is in many aspects analogous to L1. 相似文献
19.
Formal concept analysis (FCA) associates a binary relation between a set of objects and a set of properties to a lattice of
formal concepts defined through a Galois connection. This relation is called a formal context, and a formal concept is then
defined by a pair made of a subset of objects and a subset of properties that are put in mutual correspondence by the connection.
Several fuzzy logic approaches have been proposed for inducing fuzzy formal concepts from L-contexts based on antitone L-Galois connections. Besides, a possibility-theoretic reading of FCA which has been recently proposed allows us to consider
four derivation powerset operators, namely sufficiency, possibility, necessity and dual sufficiency (rather than one in standard
FCA). Classically, fuzzy FCA uses a residuated algebra for maintaining the closure property of the composition of sufficiency
operators. In this paper, we enlarge this framework and provide sound minimal requirements of a fuzzy algebra w.r.t. the closure
and opening properties of antitone L-Galois connections as well as the closure and opening properties of isotone L-Galois connections. We apply these results to particular compositions of the four derivation operators. We also give some
noticeable properties which may be useful for building the corresponding associated lattices. 相似文献
20.
We study the scattering theory for the Maxwell-Schrödinger equations
under the Coulomb gauge and the Lorentz gauge conditions in three space dimensions.
These equations belong to the borderline between the short range case and
the long range one. We prove the existence of modified wave operators for those
equations for small scattered states with no restriction on the support of the Fourier
transform of them.
Communicated by Vincent Rivasseau
submitted 14/11/02, accepted: 29/04/03 相似文献