Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Morse-Smale index theorems for elliptic boundary deformation problems.
2012
AbstractMorse-type index theorems for self-adjoint elliptic second order boundary value problems arise as the second variation of an energy functional corresponding to some variational problem. The celebrated Morse index theorem establishes a precise relation between the Morse index of a geodesic (as critical point of the geodesic action functional) and the number of conjugate points along the curve. Generalization of this theorem to linear elliptic boundary value problems appeared since seventies. (See, for instance, Smale (1965) [12], Uhlenbeck (1973) [15] and Simons (1968) [11] among others.) The aim of this paper is to prove a Morse–Smale index theorem for a second order self-adjoint el…
A metric characterization of Carnot groups
2013
We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically homogeneous.
The volume of geodesic balls and tubes about totally geodesic submanifolds in compact symmetric spaces
1997
AbstractLet M be a compact Riemannian symmetric space. We give an analytical expression for the area and volume functions of geodesic balls in M and for the area and volume functions of tubes around some totally geodesic submanifolds P of M. We plot the graphs of these functions for some compact irreducible Riemannian symmetric spaces of rank two.
On the Existence and Structure of Ψ*-Algebras of Totally Characteristic Operators on Compact Manifolds with Boundary
1999
As a contribution to the pseudodifferential analysis on manifolds with singularities we construct for each smooth, compact manifold X with boundary a Ψ*-algebra A(b)∞(X, bΩ1/2)⊆L(ϱbL2(X, bΩ1/2)) containing the algebra Ψ0b, cl(X, bΩ1/2) of totally characteristic pseudodifferential operators introduced by Melrose [25] in 1981 as a dense subalgebra; further, there is a homomorphism τ(b)A: A(b)∞(X, bΩ1/2)→Q(b)Ψ characterizing the Fredholm property of a∈A(b)∞(X, bΩ1/2) by means of the invertibility of τ(b)A(a)∈Q(b)Ψ, where Q(b)Ψ is an algebra of C∞-symbols reflecting the smooth structure of the manifold X. The Fredholm inverses of Fredholm operators in A(b)∞(X, bΩ1/2) are again in the algebra A(…
Canonical Brownian Motion on the Diffeomorphism Group of the Circle
2002
AbstractFor infinitesimal data given on the group of diffeomorphism of the circle with respect to the metric H3/2, the associated Brownian motion has been constructed by Malliavin (C.R. Acad. Sci. Parist.329 (1999), 325–329). In this work, we shall give another approach and prove the invariance of heat measures under the adjoint action of S1.
Inner functions and local shape of orthonormal wavelets
2011
Abstract Conditions characterizing all orthonormal wavelets of L 2 ( R ) are given in terms of suitable orthonormal bases (ONBs) related with the translation and dilation operators. A particular choice of the ONBs, the so-called Haar bases, leads to new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces articulate the structure of these families. The new algorithms focus on the local shape of the wavelet.
A new full descriptive characterization of Denjoy-Perron integral
1995
It is proved that the absolute continuity of the variational measure generated by an additive interval function \(F\) implies the differentiability almost everywhere of the function \(F\) and gives a full descriptive characterization of the Denjoy-Perron integral.
Radon–Nikodým Theorems for Finitely Additive Multimeasures
2015
In this paper we deal with interval multimeasures. We show some Radon–Nikodým theorems for such multimeasures using multivalued Henstock or Henstock–Kurzweil–Pettis derivatives. We do not use the separability assumption in the results.
Multiplizit�ten ?unendlich-ferner? Spitzen
1979
LetX be the quotient of a bounded symmetric domainD by an arithmetically defined subgroup Γ of all analytic automorphisms ofD and letX * be theSatake-compactification ofX. In the present note, the multiplicities of the local rings of the zero-dimensional boundary components ofX * will be computed in a completely elementary manner using reduction-theory in selfadjoint homogeneous cones.
The deformation multiplicity of a map germ with respect to a Boardman symbol
2001
We define the deformation multiplicity of a map germ f: (Cn, 0) → (Cp, 0) with respect to a Boardman symbol i of codimension less than or equal to n and establish a geometrical interpretation of this number in terms of the set of Σi points that appear in a generic deformation of f. Moreover, this number is equal to the algebraic multiplicity of f with respect to i when the corresponding associated ring is Cohen-Macaulay. Finally, we study how algebraic multiplicity behaves with weighted homogeneous map germs.