Related papers: A converse extrapolation theorem for translation i…

We extend the modular invariance property of the trace functions of vertex operator algebra on the set of irreducible modules (Zhu's theory) to the case of trace functions of intertwining operators.

We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.

We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…

In this communication, we address the problem of approximating the atoms of a parametric dictionary, commonly encountered in the context of sparse representations in "continuous" dictionaries. We focus on the case of translation-invariant…

Reverse order law for the Moore-Penrose inverses of tensors are useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-Penrose inverse of tensors. We then obtain a few necessary…

We prove a conjecture of Johann Cigler on shifted Hankel determinants.

In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of…

In this paper, we first give an expression for the Moore-Penrose inverse of the product of two tensors via the Einstein product. We then introduce a new generalized inverse of a tensor called product Moore-Penrose inverse. A necessary and…

We prove inversion of adjunction on log canonicity.

In this paper we study boundedness of translation invariant operators in the discrete space $\ell^p(\mathbb{Z}^d)$. In this context a Mikhlin type multiplier theorem is given, yielding boundedness for certain known operators . We also give…

We give a counterexample of Morrison's cone conjecture for a strict Calabi-Yau threefold.

Invariance to spatial transformations such as translations and rotations is a desirable property and a basic design principle for classification neural networks. However, the commonly used convolutional neural networks (CNNs) are actually…

We give a new proof of the sharp form of Young's inequality for convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BL]. The latter also proved a sharp reverse inequality in the case of exponents less than $1$. Our proof is…

The Rubio de Francia extrapolation theorem is a very powerful result which states that in order to show that certain operators satisfy weighted norm inequalities with Muckenhoupt weights it suffices to see that the corresponding…

We prove an operator inequality that extends strong subadditivity of entropy: after taking a trace, the operator inequality becomes the strong subadditivity of entropy.

A version of Jonsson's theorem, as previously generalized, holds in non-modular varieties.

In [6] Cho and Tanahashi showe new spectral mapping theorem of the taylor spectrum for doubly commuting pairs of p-hyponormal operators and log-hyponormal operators. In this paper, we will show that same spectral mapping theorem holds for…

Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…

This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a…

We prove a combination theorem for PD(n)-pairs.