Related papers: An abstract Coifman-Rochberg-Weiss commutator theo…
For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.
We present a short proof of the gauge invariant uniqueness theorem for relative Cuntz-Pimsner algebras of C*-correspondences.
A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with…
The purpose of this paper is to show that the Rudin-Carleson interpolation theorem is a direct corollary of Fatou's much older interpolation theorem (of 1906).
We formalise and mechanise a construtive, proof theoretic proof of Craig's Interpolation Theorem in Isabelle/HOL. We give all the definitions and lemma statements both formally and informally. We also transcribe informally the formal…
Let $f$ be a $r\times m$-matrix of holomorphic functions that is generically surjective. We provide explicit integral representation of holomorphic $\psi$ such that $\phi=f\psi$, provided that $\phi$ is holomorphic and annihilates a certain…
We prove the converse of Yano's extrapolation theorem for translation invariant operators.
In this paper, first, we introduce a notion of modified Rota-Baxter Lie algebras of weight $\mathrm{\lambda}$ with derivations (or simply modified Rota-Baxter LieDer pairs) and their representations. Moreover, we investigate cohomologies of…
We explain a connection between the combinatorial Kashiwara-Vergne conjecture and the Kontsevich formula for quantization of Poisson manifolds
Rochberg's coboundary theorem provides conditions under which the equation $(I-T)y = x$ is solvable in $y$. Here $T$ is a unilateral shift on Hilbert space, $I$ is the identity operator and $x$ is a given vector. The conditions are…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
We propose an interpolation formula for the distribution of the reflection coefficient in the presence of time reversal symmetry for chaotic cavities with absorption. This is done assuming a similar functional form as that when time…
We present a method to compute integral cohomology of posets. This toolbox is applicable as soon as the sub-posets under each object possess certain structure. This is the case for simplicial complexes and simplex-like posets. The method is…
We consider Fokker-Planck equations that interpolate a pair of supersymmetrically related Fokker-Planck equations with constant coefficients. Based on the interesting property of shape-invariance, various one-parameter interpolations of the…
In this work, we show that the complex interpolation space is the same by the two methods.
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
In this short note we explain why the log-Brunn-Minkowski conjecture is correct for complex convex bodies. We do this by relating the conjecture to the notion of complex interpolation, and appealing to a general theorem by…
Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.
We prove a Riemann-Roch formula for deformation quantization of complex manifolds and its corollary, an index theorem for elliptic pairs conjectured by Schapira and Schneiders.
We construct a decomposition of the identity operator on a Riemannian manifold $M$ as a sum of smooth orthogonal projections subordinate to an open cover of $M$. This extends a decomposition of the real line by smooth orthogonal projection…