Related papers: Infinite dimensional Cauchy-Kowalevski and Holmgre…
Quantitative algebras are algebras enriched in the category $\mathsf{Met}$ of metric spaces so that all operations are nonexpanding. Mardare, Plotkin and Panangaden introduced varieties (aka $1$-basic varieties) as classes of quantitative…
We introduce a class of almost homogeneous varieties contained in the class of spherical varieties and containing horospherical varieties as well as complete symmetric varieties. We develop K{\"a}hler geometry on these varieties, with…
In this article, we introduce classes of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function p(.) that is summable with respect to measure. These classes of…
We study the Kowalevski expansions near singularities of the swinging Atwood's machine. We show that there is a infinite number of mass ratios $M/m$ where such expansions exist with the maximal number of arbitrary constants. These…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
We prove smoothing properties and optimal Schauder type estimates for a class of nonautonomous evolution equations driven by time dependent Ornstein-Uhlenbeck operators in a separable Hilbert space. They arise as Kolmogorov equations of…
The Polchinski equations for the Wilsonian renormalization group in the $D$--dimensional matrix scalar field theory can be written at large $N$ in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension…
We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in…
The standard Hamiltonian machinery, being applied to field theory, leads to infinite-dimensional phase spaces. It is not covariant. In this article, we present covariant finite-dimensional multimomentum Hamiltonian formalism for field…
Taking into account the global one-dimensionality conjecture recently proposed by the author, the Cauchy-like analytical wave functional of the Wheeler-DeWitt theory is derived. The crucial point of the integration strategy is canceling of…
We provide extension procedures for nonlinear expectations to the space of all bounded measurable functions. We first discuss a maximal extension for convex expectations which have a representation in terms of finitely additive measures.…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
Let $\mathfrak g$ be an infinite-dimensional Lie algebra, and $G$ be the algebraic completion of a $\mathfrak g$-module. Using the geometric model of Schottky uniformization of Riemann sphere to obtain a higher genus Riemann surface, we…
We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes, the class of $\cC^\infty$ functions definable in a…
In this paper, we establish a Bloch-type growth theorem for generalized Bloch-type spaces and discuss relationships between Dirichlet-type spaces and Hardy-type spaces on certain classes of complex-valued functions. Then we present some…
An integro-differential Kolmogorov equation is considered in H\"{o}lder-type spaces defined by a scalable L\'{e}vy measure. Some properties of those spaces and estimates of the solution are derived using probabilistic representations.
Under the assumption that orthogonal polynomials of several variables admit an addition formula, we can define a convolution structure and use it to study the Fourier orthogonal expansions on a homogeneous space. We define a maximal…
The left and right homological integrals are introduced for a large class of infinite dimensional Hopf algebras. Using the homological integrals we prove a version of Maschke's theorem for infinite dimensional Hopf algebras. The…
High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of…
We use non-standard analysis to define a category $^\star\!\operatorname{Hilb}$ suitable for categorical quantum mechanics in arbitrary separable Hilbert spaces, and we show that standard bounded operators can be suitably embedded in it. We…