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Author: Marco Bramanti
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 136
ISBN-13: 0821849034
DOWNLOAD EBOOK"March 2010, Volume 204, number 961 (end of volume)."
Author: Marco Bramanti
Publisher: Springer Science & Business Media
Published: 2013-11-20
Total Pages: 157
ISBN-13: 3319020870
DOWNLOAD EBOOKHörmander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients, which have been intensively studied since the late 1960s and are still an active field of research. This text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development.
Author: Brian Street
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2023-07-03
Total Pages: 768
ISBN-13: 3111085643
DOWNLOAD EBOOKMaximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.
Author: Klaus Thomsen
Publisher: American Mathematical Soc.
Published: 2010-06-11
Total Pages: 138
ISBN-13: 0821846922
DOWNLOAD EBOOKThe author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.
Author: Matthew J. Gursky
Publisher: Springer
Published: 2009-07-31
Total Pages: 296
ISBN-13: 364201674X
DOWNLOAD EBOOKThis volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.
Author: Montserrat Casals-Ruiz
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 168
ISBN-13: 0821852582
DOWNLOAD EBOOK"Volume 212, number 999 (end of volume)."
Author: Michael Thoreau Lacey
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 87
ISBN-13: 0821845403
DOWNLOAD EBOOK"Volume 205, number 965 (fourth of 5 numbers)."
Author: Steve Hofmann
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 91
ISBN-13: 0821852388
DOWNLOAD EBOOKLet $X$ be a metric space with doubling measure, and $L$ be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on $L^2(X)$. In this article the authors present a theory of Hardy and BMO spaces associated to $L$, including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Further specializing to the case that $L$ is a Schrodinger operator on $\mathbb{R}^n$ with a non-negative, locally integrable potential, the authors establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, they define Hardy spaces $H^p_L(X)$ for $p>1$, which may or may not coincide with the space $L^p(X)$, and show that they interpolate with $H^1_L(X)$ spaces by the complex method.
Author: Giovanna Citti
Publisher: Springer
Published: 2015-10-31
Total Pages: 381
ISBN-13: 3319026666
DOWNLOAD EBOOKThe analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications.
Author: Peter O'Sullivan
Publisher: American Mathematical Soc.
Published: 2010-08-06
Total Pages: 135
ISBN-13: 082184895X
DOWNLOAD EBOOKThe author considers homomorphisms $H \to K$ from an affine group scheme $H$ over a field $k$ of characteristic zero to a proreductive group $K$. Using a general categorical splitting theorem, Andre and Kahn proved that for every $H$ there exists such a homomorphism which is universal up to conjugacy. The author gives a purely group-theoretic proof of this result. The classical Jacobson-Morosov theorem is the particular case where $H$ is the additive group over $k$. As well as universal homomorphisms, the author considers more generally homomorphisms $H \to K$ which are minimal, in the sense that $H \to K$ factors through no proper proreductive subgroup of $K$. For fixed $H$, it is shown that the minimal $H \to K$ with $K$ reductive are parametrised by a scheme locally of finite type over $k$.
