Related papers: Towards Empirical Process Theory for Vector-Valued…

We study the compact embedding between smoothness Morrey spaces on bounded domains and characterise its entropy numbers. Here we discover a new phenomenon when the difference of smoothness parameters in the source and target spaces is…

Given a general scalar balance law, i.e., in several space dimensions and with flux and source both space and time dependent, we focus on the functional properties of the entropy production. We apply this operator to entropy solutions, to…

Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A…

In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces. Metric entropy characterizes the information complexity of function…

This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…

In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…

The main objective of this paper is to extend Morse-Forman theory to vector-valued functions. This is mostly motivated by the need to develop new tools and methods to compute multiparameter persistence. To generalize the theory, in addition…

Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic…

Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…

The Hardy space $H^{p}$ of vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ and with values in Banach space are defined. Vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ with values in Hilbert space…

Rademacher theorem asserts that Lipschitz continuous functions between Euclidean spaces are differentiable almost everywhere. In this work we extend this result to set-valued maps using an adequate notion of set-valued differentiability…

This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…

In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators.…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…

We lift ambit fields as introduced by Barndorff-Nielsen and Schmiegel to a class of Hilbert space-valued volatility modulated Volterra processes. We name this class Hambit fields, and show that they can be expressed as a countable sum of…

We present a framework to derive risk bounds for vector-valued learning with a broad class of feature maps and loss functions. Multi-task learning and one-vs-all multi-category learning are treated as examples. We discuss in detail…

This is a note on the graphs of two smooth real-valued functions in the plane with no intersection and the natural map onto the region surrounded by them with the canonical projection to the line composed, yielding its Reeb space. The Reeb…

In the field of natural language processing (NLP), continuous vector representations are crucial for capturing the semantic meanings of individual words. Yet, when it comes to the representations of sets of words, the conventional…