Algebras Of Singular Integral Operators With Kernels Controlled By Multiple Norms
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Algebras Of Singular Integral Operators With Kernels Controlled By Multiple Norms
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Author : Alexander Nagel
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-08
Algebras Of Singular Integral Operators With Kernels Controlled By Multiple Norms written by Alexander Nagel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Mathematics categories.
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.
Maximal Functions Littlewood Paley Theory Riesz Transforms And Atomic Decomposition In The Multi Parameter Flag Setting
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Author : Yongsheng Han
language : en
Publisher: American Mathematical Society
Release Date : 2022-08-31
Maximal Functions Littlewood Paley Theory Riesz Transforms And Atomic Decomposition In The Multi Parameter Flag Setting written by Yongsheng Han and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-31 with Mathematics categories.
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Moufang Sets And Structurable Division Algebras
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Author : Lien Boelaert
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-10
Moufang Sets And Structurable Division Algebras written by Lien Boelaert and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-10 with Mathematics categories.
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.
Moufang Loops And Groups With Triality Are Essentially The Same Thing
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Author : J. I. Hall
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-05
Moufang Loops And Groups With Triality Are Essentially The Same Thing written by J. I. Hall and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-05 with Mathematics categories.
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.”
Generalized Mercer Kernels And Reproducing Kernel Banach Spaces
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Author : Yuesheng Xu
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-10
Generalized Mercer Kernels And Reproducing Kernel Banach Spaces written by Yuesheng Xu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Mathematics categories.
This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .
Time Changes Of The Brownian Motion Poincar Inequality Heat Kernel Estimate And Protodistance
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Author : Jun Kigami
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-10
Time Changes Of The Brownian Motion Poincar Inequality Heat Kernel Estimate And Protodistance written by Jun Kigami and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-10 with Mathematics categories.
In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0,1]n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0,1]n, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on [0,1]2 and self-similar measures. The author shows the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, he obtains diagonal lower and upper estimates of the heat kernel as time tends to 0. In particular, to express the principal part of the lower diagonal heat kernel estimate, he introduces “protodistance” associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub-Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown.
Crossed Products Of Operator Algebras
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Author : Elias G. Katsoulis
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-10
Crossed Products Of Operator Algebras written by Elias G. Katsoulis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Mathematics categories.
The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.
Spinors On Singular Spaces And The Topology Of Causal Fermion Systems
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Author : Felix Finster
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-10
Spinors On Singular Spaces And The Topology Of Causal Fermion Systems written by Felix Finster and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-10 with Mathematics categories.
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.
Matrix Functions Of Bounded Type An Interplay Between Function Theory And Operator Theory
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Author : Raúl E. Curto
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-05
Matrix Functions Of Bounded Type An Interplay Between Function Theory And Operator Theory written by Raúl E. Curto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-05 with Mathematics categories.
In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. They propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér Interpolation Problem for matrix rational functions. The authors then extend the H∞-functional calculus to an H∞¯¯¯¯¯¯¯¯¯+H∞-functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmos's Problem 5 and then establish a matrix-valued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of 2×2 partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.
Algebraic Geometry Over C Rings
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Author : Dominic Joyce
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-05
Algebraic Geometry Over C Rings written by Dominic Joyce and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-05 with Mathematics categories.
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”.