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The concept of adjusted sublevel set for a quasiconvex function was introduced in \cite{AuHa05} and the local existence of a norm-to-weak$^*$ upper semicontinuous base-valued submap of the normal operator associated to the adjusted sublevel…
Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.
We introduce the notion of envelope of a topological algebra (in particular, an arbitrary associative algebra) with respect to a class of Banach algebras. In the case of the class of real Banach algebras of polynomial growth, i.e.,…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
Our paper is a complement to a recent article by D. Azagra and C. Mudarra (2021). We show how older results on semiconvex functions with modulus $\omega$ easily imply extension theorems for $C^{1,\omega}$-smooth functions on super-reflexive…
We deal with the existence of weak solutions for a mixed Neumann-Robin-Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We…
After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux…
We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a…
We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form \( du_t -L_t(u_t)u_t dt = N_t(u_t)dt + F(u_t)\cdot d\mathbf X_t \), where \( \mathbf X\) is a \( \gamma\)-H\"older rough path for…
We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators $A_j$ on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also…
We construct an explicit transitive free action of a Banach space of H\"older functions on the space of branched rough paths, which yields in particular a bijection between theses two spaces. This endows the space of branched rough paths…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
We show that well-established methods from the theory of Banach modules and time-frequency analysis allow to derive completeness results for the collection of shifted and dilated version of a given (test) function in a quite general…
We develop an ind-Banach framework for revisiting analytification in complex geometry, inspired by Bambozzi-Chiarellotto-Vanni's work on tempered cohomology. We define several ind-Banach rings of overconvergent and holomorphic power series…
The main purpose of this paper is to develop some methods to investigate the Schwarz type lemmas of holomorphic mappings and pluriharmonic mappings in Banach spaces. Initially, we extend the classical Schwarz lemmas of holomorphic mappings…
We present new results concerning the solvability, of lack thereof, in the Cauchy problem for the debar operator, with initial values assigned on a weakly pseudoconvex hypersurface, and provide illustrative examples.
We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, roughly speaking of the type of the exponential of a power of the distance from the origin. We…
This paper introduces a notion of differential forms on closed, potentially fractal, subsets of Euclidean space by defining pointwise cotangent spaces using the restriction of $C^1$ functions to this set. Aspects of cohomology are…
We give a self-contained and simplified presentation of the theory of covariant representations for inverse semigroup actions on Banach algebras, which was recently introduced in the authors and A. Mckee in the twisted case. The main result…
The notion of super weak compactness for subsets of Banach spaces is a strengthening of the weak compactness that can be described as a local version of super-reflexivity. A recent result of K. Tu which establishes that the closed convex…