Algebras Of Singular Integral Operators With Kernels Controlled By Multiple Norms

Author : Alexander Nagel
Publisher : American Mathematical Soc.
ISBN 13 : 1470434385
Total Pages : 141 pages
Book Rating : 4.80/5 ( download)

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Download or read book Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms written by Alexander Nagel and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study algebras of singular integral operators on R and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on for . . While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.

Author : Yongsheng Han
Publisher : American Mathematical Society
ISBN 13 : 1470453452
Total Pages : 118 pages
Book Rating : 4.59/5 ( download)

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Download or read book Maximal Functions, Littlewood–Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-Parameter Flag Setting written by Yongsheng Han and published by American Mathematical Society. This book was released on 2022-08-31 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Author : Felix Finster
Publisher : American Mathematical Soc.
ISBN 13 : 1470436213
Total Pages : 83 pages
Book Rating : 4.16/5 ( download)

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Download or read book Spinors on Singular Spaces and the Topology of Causal Fermion Systems written by Felix Finster and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples such as the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.

Author : Charles Collot
Publisher : American Mathematical Soc.
ISBN 13 : 1470436264
Total Pages : 93 pages
Book Rating : 4.61/5 ( download)

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Download or read book On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation written by Charles Collot and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the energy super critical semilinear heat equation The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data using energy bounds. The whole scheme draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.

Author : J. I. Hall
Publisher : American Mathematical Soc.
ISBN 13 : 1470436221
Total Pages : 186 pages
Book Rating : 4.23/5 ( download)

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Download or read book Moufang Loops and Groups with Triality are Essentially the Same Thing written by J. I. Hall and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1925 Élie Cartan introduced the principal of triality specifically for the Lie groups of type D4, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was in turn motivated by the work of George Glauberman from 1968. Here the author makes the statement precise in a categorical context. In fact the most obvious categories of Moufang loops and groups with triality are not equivalent, hence the need for the word “essentially.”

Author : Lien Boelaert
Publisher : American Mathematical Soc.
ISBN 13 : 1470435543
Total Pages : 90 pages
Book Rating : 4.47/5 ( download)

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Download or read book Moufang Sets and Structurable Division Algebras written by Lien Boelaert and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group. It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. The authors extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, they show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field k of characteristic different from 2 and 3 arises from a structurable division algebra. The authors also obtain explicit formulas for the root groups, the τ-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups.

Author : Dominic Joyce
Publisher : American Mathematical Soc.
ISBN 13 : 1470436450
Total Pages : 139 pages
Book Rating : 4.52/5 ( download)

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Download or read book Algebraic Geometry over C∞-Rings written by Dominic Joyce and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.

Author : Yulia Karpeshina
Publisher : American Mathematical Soc.
ISBN 13 : 1470435438
Total Pages : 139 pages
Book Rating : 4.31/5 ( download)

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Download or read book Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two written by Yulia Karpeshina and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a Schrödinger operator H=−Δ+V(x⃗ ) in dimension two with a quasi-periodic potential V(x⃗ ). They prove that the absolutely continuous spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves ei⟨ϰ⃗ ,x⃗ ⟩ in the high energy region. Second, the isoenergetic curves in the space of momenta ϰ⃗ corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor type structure). A new method of multiscale analysis in the momentum space is developed to prove these results. The result is based on a previous paper on the quasiperiodic polyharmonic operator (−Δ)l+V(x⃗ ), l>1. Here the authors address technical complications arising in the case l=1. However, this text is self-contained and can be read without familiarity with the previous paper.

Author : Viktoria Heu
Publisher : American Mathematical Soc.
ISBN 13 : 1470435667
Total Pages : 103 pages
Book Rating : 4.60/5 ( download)

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Download or read book Flat Rank Two Vector Bundles on Genus Two Curves written by Viktoria Heu and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section. As a particularity of the genus case, connections as above are invariant under the hyperelliptic involution: they descend as rank logarithmic connections over the Riemann sphere. The authors establish explicit links between the well-known moduli space of the underlying parabolic bundles with the classical approaches by Narasimhan-Ramanan, Tyurin and Bertram. This allows the authors to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical -configuration of the Kummer surface. The authors also recover a Poincaré family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. They explicitly compute the Hitchin integrable system on the moduli space of Higgs bundles and compare the Hitchin Hamiltonians with those found by van Geemen-Previato. They explicitly describe the isomonodromic foliation in the moduli space of vector bundles with -connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.

Author : William Goldman
Publisher : American Mathematical Soc.
ISBN 13 : 1470436140
Total Pages : 78 pages
Book Rating : 4.48/5 ( download)

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Download or read book Automorphisms ofTwo-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane written by William Goldman and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: The automorphisms of a two-generator free group F acting on the space of orientation-preserving isometric actions of F on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group on by polynomial automorphisms preserving the cubic polynomial and an area form on the level surfaces .