Higher Moments of Banach Space Valued Random Variables
Higher Moments of Banach Space Valued Random Variables

Author: Svante Janson

Publisher: American Mathematical Soc.

Published: 2015-10-27

Total Pages: 124

ISBN-13: 1470414651

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The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.

An Introduction to Computational Stochastic PDEs
An Introduction to Computational Stochastic PDEs

Author: Gabriel J. Lord

Publisher: Cambridge University Press

Published: 2014-08-11

Total Pages: 516

ISBN-13: 0521899907

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This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.

Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces
Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces

Author: Ariel Barton:

Publisher: American Mathematical Soc.

Published: 2016-09-06

Total Pages: 122

ISBN-13: 1470419890

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This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Lp classes. The authors establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given Lp space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.

Nil Bohr-Sets and Almost Automorphy of Higher Order
Nil Bohr-Sets and Almost Automorphy of Higher Order

Author: Wen Huang

Publisher: American Mathematical Soc.

Published: 2016-04-26

Total Pages: 98

ISBN-13: 147041872X

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Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d∈N does the collection of {n∈Z:S∩(S−n)∩…∩(S−dn)≠∅} with S syndetic coincide with that of Nild Bohr0 -sets? In the second part, the notion of d -step almost automorphic systems with d∈N∪{∞} is introduced and investigated, which is the generalization of the classical almost automorphic ones.

Classes of Polish Spaces Under Effective Borel Isomorphism
Classes of Polish Spaces Under Effective Borel Isomorphism

Author: Vassilios Gregoriades

Publisher: American Mathematical Soc.

Published: 2016-03-10

Total Pages: 102

ISBN-13: 1470415631

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The author studies the equivalence classes under Δ11 isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of Δ11-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.

Moduli of Double EPW-Sextics
Moduli of Double EPW-Sextics

Author: Kieran G. O'Grady

Publisher: American Mathematical Soc.

Published: 2016-03-10

Total Pages: 188

ISBN-13: 1470416964

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The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of ⋀3C6 modulo the natural action of SL6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3[2] polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds.

Classification of $E_0$-Semigroups by Product Systems
Classification of $E_0$-Semigroups by Product Systems

Author: Michael Skeide

Publisher: American Mathematical Soc.

Published: 2016-03-10

Total Pages: 138

ISBN-13: 1470417383

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In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.

The Fourier Transform for Certain HyperKahler Fourfolds
The Fourier Transform for Certain HyperKahler Fourfolds

Author: Mingmin Shen

Publisher: American Mathematical Soc.

Published: 2016-03-10

Total Pages: 178

ISBN-13: 1470417405

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Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle representing the Beauville-Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of Hyperkähler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.

Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations
Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations

Author: Volker Bach

Publisher: American Mathematical Soc.

Published: 2016-03-10

Total Pages: 134

ISBN-13: 1470417057

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The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket-Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.