Related papers: Embeddings of $\alpha$-modulation spaces

Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…

We study embeddings $J \rightarrow G$ of simple linear algebraic groups with the following property: the simple components of the $J$ module Lie($G$)/Lie($J$) are all minuscule representations of $J$. One family of examples occurs when the…

Recent studies have revealed that neural networks learn interpretable algorithms for many simple problems. However, little is known about how these algorithms emerge during training. In this article, I study the training dynamics of a small…

Necessary and sufficient conditions are presented for a fractional Orlicz-Sobolev space on $\rn$ to be continuously embedded into a space of uniformly continuous functions. The optimal modulus of continuity is exhibited whenever these…

It is well known that Sobolev embeddings can be improved in the presence of symmetries. In this article, we considere the situation in which given a domain $\Omega=\Omega_1 \times \Omega_2$ in $\mathbb{R}^N$ with a cylindrical symmetry, and…

In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Haj{\l}asz-Triebel-Lizorkin and Haj{\l}asz-Besov spaces in the general context…

We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…

While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…

Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. While achieving competitive performance on a variety of network inference tasks such as node classification and link prediction, these…

It is shown that the modulation spaces $M_{p}^{w}$ can be characterized by the approximation behavior of their elements using Local Fourier bases. In analogy to the Local Fourier bases, we show that the modulation spaces can also be…

We prove sharp embedding inequalities for certain reduced Sobolev spaces that arise naturally in the context of Dirichlet problems with $L^1$ data. We also find the optimal target spaces for such embeddings, which in dimension 2 could be…

Let A be an algebra with a countable basis and let B be, say, a Frechet algebra that contains A as a dense subalgebra. This embedding induces a functor from the derived category of B-modules to the derived category of A-modules. In many…

We consider the principal subspaces of certain level $k\geqslant 1$ integrable highest weight modules and generalized Verma modules for the untwisted affine Lie algebras in types $D$, $E$ and $F$. Generalizing the approach of G. Georgiev we…

The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. We include two appendices, one on the relation…

We introduce two Bishop-Phelps-Bollob\'as moduli which measure, for a given Banach space, what is the best possible Bishop-Phelps-Bollob\'as theorem in this space. We show that there is a common upper bound for these moduli for all Banach…

We prove compactness of the embeddings in Sobolev spaces for fractional super and sub harmonic functions with radial symmetry. The main tool is a pointwise decay for radially symmetric functions belonging to a function space defined by…

We extend the definition of alpha space as introduced in [1] to two spacetime dimensions. We discuss how this can be used to find conformal block decompositions of known functions and how to easily recover several lightcone bootstrap…

In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…

We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…

We give infinitely many new isomorphisms between moduli spaces of bundles on local surfaces and on local Calabi--Yau threefolds.