Geodesics Retracts And The Norm Preserving Extension Property In The Symmetrized Bidisc
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Geodesics Retracts And The Norm Preserving Extension Property In The Symmetrized Bidisc
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Author : Jim Agler
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-10
Geodesics Retracts And The Norm Preserving Extension Property In The Symmetrized Bidisc written by Jim Agler 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.
A set V in a domain U in Cn has the norm-preserving extension property if every bounded holomorphic function on V has a holomorphic extension to U with the same supremum norm. We prove that an algebraic subset of the symmetrized bidisc
Geodesics Retracts And The Norm Preserving Extension Property In The Symmetrized Bidisc
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Author : Jim Agler
language : en
Publisher:
Release Date : 2019
Geodesics Retracts And The Norm Preserving Extension Property In The Symmetrized Bidisc written by Jim Agler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
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”.
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.”
On The Stability Of Type I Blow Up For The Energy Super Critical Heat Equation
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Author : Charles Collot
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-05
On The Stability Of Type I Blow Up For The Energy Super Critical Heat Equation written by Charles Collot 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.
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.
Compact Quotients Of Cahen Wallach Spaces
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Author : Ines Kath
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-13
Compact Quotients Of Cahen Wallach Spaces written by Ines Kath 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 2020-02-13 with Education categories.
Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.
Automorphisms Of Fusion Systems Of Finite Simple Groups Of Lie Type
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Author : Carles Broto
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-13
Automorphisms Of Fusion Systems Of Finite Simple Groups Of Lie Type written by Carles Broto 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 2020-02-13 with Education categories.
For a finite group G of Lie type and a prime p, the authors compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from Out(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of BG∧p in terms of Out(G).
Quasi Periodic Standing Wave Solutions Of Gravity Capillary Water Waves
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Author : Massimiliano Berti
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-03
Quasi Periodic Standing Wave Solutions Of Gravity Capillary Water Waves written by Massimiliano Berti 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 2020-04-03 with Education categories.
The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces
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Author : Luigi Ambrosio
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-13
Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces written by Luigi Ambrosio 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 2020-02-13 with Education categories.
The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.