Related papers: Donald Burkholder's work in martingales and analys…
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
We discuss some conjectural inequalities that are related to singular integrals, martingales, quasiconformal mappings, and the calculus of variations. Specifically, we present evidence for a conjecture of Iwaniec concerning the best…
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
This is a reference volume on polyfold and Fredholm theory.
Annotated bibliography of 18th, 19th, and early 20th century works involving Lambert series. A tour of 19th and early 20th century analytic number theory.
Recent results on the analytical evaluation of double-box Feynman integrals and the corresponding methods of evaluation are briefly reviewed.
This is a translation of Heinz Bachmann's influential paper, wherein the Bachmann-Howard ordinal is defined, and some general considerations given on systems of ordinal functions. Permission to post has been granted by the editors of…
This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.
A general device is proposed, which provides for extension of exponential inequalities for sums of independent real-valued random variables to those for martingales in the 2-smooth Banach spaces. This is used to obtain optimum bounds of the…
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
Given a probability space $(\Omega, \mathsf{A}, \mu)$, let $\mathsf{A}_1, \mathsf{A}_2, ...$ be a filtration of $\sigma$-subalgebras of $\mathsf{A}$ and let $\mathsf{E}_1, \mathsf{E}_2, ...$ denote the corresponding family of conditional…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
Construction of analytic functions, which determine bounded Toeplitz operators
Discussion of ``Statistical analysis of an archeological find'' by Andrey Feuerverger [arXiv:0804.0079]
We provide generalizations of Burkholder's inequalities involving conditioned square functions of martingales to the general context of martingales in noncommutative symmetric spaces. More precisely, we prove that Burkholder's inequalities…
Quaternion analysis is considered in full details where a new analyticity condition in complete analogy to complex analysis is found. The extension to octonions is also worked out.
We survey some recent developments in the analytic theory of multiple Dirichlet series with arithmetical coefficients on the numerators.
This note proposes a procedure for enhancing the quality of probabilistic prediction algorithms via betting against their predictions. It is inspired by the success of the conformal test martingales that have been developed recently.
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.