Search results for "RACE"
showing 10 items of 4458 documents
Dyadic Norm Besov-Type Spaces as Trace Spaces on Regular Trees
2019
In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces.
Notions of Dirichlet problem for functions of least gradient in metric measure spaces
2019
We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazón-Rossi–De León, solutions by considering the Dirichlet problem for p-harmonic functions, p>1, and letting p→1. Tools developed and used in this paper include the inner perimeter measure of a domain. Peer reviewed
Hitchhiker's guide to the fractional Sobolev spaces
2012
AbstractThis paper deals with the fractional Sobolev spaces Ws,p. We analyze the relations among some of their possible definitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results.Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains.
Neumann p-Laplacian problems with a reaction term on metric spaces
2020
We use a variational approach to study existence and regularity of solutions for a Neumann p-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincare inequality. Trace theorems for functions with bounded variation are applied in the definition of the variational functional and minimizers are shown to satisfy De Giorgi type conditions.
Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds
2002
We prove that the moduli spaces A_3(D) of polarized abelian threefolds with polarizations of types D=(1,1,2), (1,2,2), (1,1,3) or (1,3,3) are unirational. The result is based on the study of families of simple coverings of elliptic curves of degree 2 or 3 and on the study of the corresponding period mappings associated with holomorphic differentials with trace 0. In particular we prove the unirationality of the Hurwitz space H_{3,A}(Y) which parameterizes simply branched triple coverings of an elliptic curve Y with determinants of the Tschirnhausen modules isomorphic to A^{-1}.
Trace Identities on Diagonal Matrix Algebras
2020
Let Dn be the algebra of n × n diagonal matrices. On such an algebra it is possible to define very many trace functions. The purpose of this paper is to present several results concerning trace identities satisfied by this kind of algebras.
Traces of weighted function spaces: dyadic norms and Whitney extensions
2017
The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.
Possible extensions of the noncommutative integral
2011
In this paper we will discuss the problem of extending a trace σ defined on a dense von Neumann subalgebra \(\mathfrak{M}\) of a topological *-algebra \({\mathfrak{A}}\) to some subspaces of \({\mathfrak{A}}\). In particular, we will prove that extensions of the trace σ that go beyond the space L1(σ) really exist and we will explicitly construct one of these extensions. We will continue the analysis undertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745–1777, 2010) on the general problem of extending positive linear functionals on a *-algebra.
Determinant Bundles over Grassmannians
1989
Denoting by H the Hilbert space of square-integrable Dirac spinor fields on a manifold M, transforming according to a unitary representation p of a gauge group G, we have a linear representation of the group g of gauge transformations in the space H. If ρ is faithful we can consider g as a subgroup of the general linear group GL(H). By constructing representations of GL(H) we automatically obtain representations of g. It turns out that in the case when the dimension d of M is odd, g is contained in a smaller group GLp ⊂ GL(H) which has the property that it perturbs the subspace H+ ⊂ H consisting of eigenvectors of a Dirac operator belonging to positive eigenvalues, by an operator A for whic…
On the Use of Metal Purine Derivatives (M=Ir, Rh) for the Selective Labeling of Nucleosides and Nucleotides
2014
The reactions of neutral or cationic IrIII and RhIII derivatives of phenyl purine nucleobases with unsymmetrical alkynes produce new metallacycles in a predictable manner, which allows for the incorporation of either photoactive (anthracene or pyrene) or electroactive (ferrocene) labels in the nucleotide or nucleoside moiety. The reported methodology (metalation of the purine derivative and subsequent marker insertion) could be used for the postfunctionalization and unambiguous labeling of oligonucleotides.