Related papers: Nevanlinna-Pick interpolation for $C+BH^\infty$

We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients,…

This paper characterises the subspaces of $H^2(\mathbb D)$ simultaneously invariant under $S^2 $ and $S^{2k+1}$, where $S$ is the unilateral shift, then further identifies the subspaces that are nearly invariant under both $(S^2)^*$ and…

We recall the derived subalgebra of a BCK-algebra, and use this to define the derived ideal. Using the derived ideal, we show that the category of commutative BCK-algebras is a reflective subcategory of the category of BCK-algebras. After…

We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for…

Let T be a C_{\cdot 0}-contraction on a Hilbert space H and S be a non-trivial closed subspace of H. We prove that S is a T-invariant subspace of H if and only if there exists a Hilbert space D and a partially isometric operator \Pi :…

In this paper we introduce a hyperbolic distance $\delta$ on the noncommutative open ball $[B(H)^n]_1$, where $B(H)$ is the algebra of all bounded linear operators on a Hilbert space $H$, which is a noncommutative extension of the…

For a Hilbert function space $\mathcal H$ the Smirnov class $\mathcal N^+(\mathcal H)$ is defined to be the set of functions expressible as a ratio of bounded multipliers of $\mathcal H$, whose denominator is cyclic for the action of…

Classical interpolation inequality of the type $\|u\|_{X}\leq C\|u\|_{Y}^{\theta}\|u\|_{Z}^{1-\theta}$ is well known in the case when $X$, $Y$, $Z$ are Lebesgue spaces. In this paper we show that this result may be extended by replacing…

We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex…

Nevanlinna-Pick interpolation developed from a topic in classical complex analysis to a useful tool for solving various problems in control theory and electrical engineering. Over the years many extensions of the original problem were…

Let $H$ be an infinite dimensional Hilbert space. We show that there exists a subspace of $B(H)$ which is isometric to $\ell_2$ and completely isometric to its antidual in the sense of the theory of operator spaces recently developed by…

We characterize the algebra $H^\infty \circ L_{m}$, where $m$ is a point of the maximal ideal space of $H^\infty$ with nontrivial Gleason part $P(m)$ and $L_{m} : \mathbb{D}\to P(m)$ is the coordinate Hoffman map. In particular, it is shown…

We give an elementary proof of Sarason's solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete parametrization of all solutions of such a problem. The…

Let $\mathcal{H}$ be Hilbert space and $(\Omega,\mu)$ a $\sigma$-finite measure space. Multiplicatively invariant (MI) spaces are closed subspaces of $ L^2(\Omega, \mathcal{H})$ that are invariant under point-wise multiplication by…

In this paper we study the space $C(\mathfrak{gl}_n(\mathbb{F}_q))$ of complex invariant functions on $\mathfrak{gl}_n(\mathbb{F}_q)$, through a Hopf algebra viewpoint. First, we consider a variant notion of Zelevinsky's PSH algebra defined…

We consider the link and three-manifold invariants from arXiv:1912.02063, which are defined in terms of certain non-semisimple finite ribbon categories $\mathcal{C}$ together with a choice of tensor ideal and modified trace. If the ideal is…

A Banach lattice E is called p-disjointly homogeneous, 1< p< infty, when every sequence of pairwise disjoint normalized elements in E has a subsequence equivalent to the unit vector basis of l_p. Employing methods from interpolation theory,…

We identify necessary and sufficient conditions on $k$th order differential operators $\mathbb{A}$ in terms of a fixed halfspace $H^+\subset\mathbb{R}^n$ such that the Gagliardo--Nirenberg--Sobolev inequality $$…

In this paper, we use a new method to solve a long-standing problem. More specifically, we show that the Beurling-type theorem holds in the Bergman space $A^2_\alpha(D)$ for any $-1<\alpha < +\infty$. That is, every invariant subspace $H$…

We consider the action of a linear subspace $U$ of $\{0,1\}^n$ on the set of AC$^0$ formulas with inputs labeled by literals in the set $\{X_1,\overline X_1,\dots,X_n,\overline X_n\}$, where an element $u \in U$ acts on formulas by…