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Skateboarding besties!
Go for a wild ride with Sunny and Rox at the Friendly Falls skateboarding contest. Lenticular book cover.
Book
Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and
operator theory. We 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. We propose a new notion of tensored-scalar singularity, and
then answer questions on Hankel operators with matrix-valued bounded type symbols. We 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. We then extend the
eBook
A career as a cosmetologist
Introduces cosmetology which offers many opportunities for people who like working with their hands and using their creativity to help others look their best.
Book
The Riesz Transform of Codimension Smaller Than One and the Wolff Energy
Fix $d\\geq 2$, and $s\\in (d-1,d)$. The authors characterize the non-negative locally finite non-atomic Borel measures $\\mu $ in $\\mathbb R^d$ for which the associated $s$-Riesz transform is bounded in $L^2(\\mu )$ in terms of the Wolff energy. This extends the range of $s$ in which the Mateu-Prat-Verdera characterization of measures with bounded $s$-Riesz transform is known. As an application, the authors give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator $(-\\Delta )^\\alpha /2$, $\\alpha \\in (1,2)$, in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions.
eBook
Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows
In this work we study strong spectral properties of Ruelle transfer operators related to a large family of Gibbs measures for contact
Anosov flows. The ultimate aim is to establish exponential decay of correlations for Hölder observables with respect to a very general
class of Gibbs measures. The approach invented in 1997 by Dolgopyat in “On decay of correlations in Anosov flows” and further developed
in Stoyanov (2011) is substantially refined here, allowing to deal with much more general situations than before, although we still
restrict ourselves to the uniformly hyperbolic case. A rather general procedure is established which produces the desired estimates
whenever the Gibbs measure admits a Pesin set with exponentially small tails, that is a Pesin set whose preimages along the flow have
measures decaying exponentially fast. We call such Gibbs measures regular. Recent results in Gouëzel and Stoyanov (2019) prove existence
of such Pesin sets for hyperbolic diffeomorphisms and flows for a large variety of Gibbs measures determined by Hölder continuous
potentials. The strong spectral estimates for Ruelle operators and well-established techniques lead to exponential decay of correlations
for Hölder continuous observables, as well as to some other consequences such as: (a) existence of a non-zero analytic continuation of
the Ruelle zeta function with a pole at the entropy in a vertical strip containing the entropy in its interior; (b) a Prime Orbit
Theorem with an exponentially small error.
eBook
Limit operators, collective compactness, and the spectral theory of infinite matrices
In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the
recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised
collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this
generalised collectively compact operator theory to the set of limit operators of an operator
eBook
Dyadic-probabilistic methods in bilinear analysis
We demonstrate and develop dyadic–probabilistic methods in connection with non-homogeneous bilinear operators, namely singular
integrals and square functions. We develop the full non-homogeneous theory of bilinear singular integrals using a modern point of view.
The main result is a new global
While proving our bilinear results we also advance and
refine the linear theory of Calderón–Zygmund operators by improving techniques and results. For example, we simplify and make more
efficient some non-homogeneous summing arguments appearing in
eBook