Related papers: Study of weaving frames in Krein spaces
We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building…
A $J$-frame for a Krein space $\mathcal{H}$ is in particular a frame for $\mathcal{H}$ (in the Hilbert space sense). But it is also compatible with the indefinite inner-product of $\mathcal{H}$, meaning that it determines a pair of maximal…
In this paper, some properties on weighted modulation and Wiener amalgam spaces are characterized by the corresponding properties on weighted Lebesgue spaces. As applications, sharp conditions for product inequalities, convolution…
We introduce the notion of weaving continuous controlled K-g-fusion frame in Hilbert space. Some characterizations of weaving continuous controlled K-g-fusion frame have been presented. We extend some of the recent results of woven…
This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach we follow in this survey uses a more abstract but very…
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…
In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a uniformly…
Thye theory of frames for a Hilbert space plays a fundamental role in signal processing, image processing, data compression, sampling theory and much more, as well as being a fruitful area of research in abstract mathematics. In this…
The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…
In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors…
Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…
This paper tackles the simultaneous optimization of pose and Neural Radiance Fields (NeRF). Departing from the conventional practice of using explicit global representations for camera pose, we propose a novel overparameterized…
A definition of frames in Krein spaces is proposed which extends the concept of $J$-frames defined by J.I. Giribet et al., J. Math. Anal. Appl. ${\textbf{393}}$ (2012), 122-137. The principal difference consists in the fact that a $J$-frame…
We study embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces. These results lead to a transfer principle that is directly applicable to tractability studies of multivariate problems as integration…
This paper extends the concepts of Minimal Redundancy Condition (MRC) and robustness of erasures for infinite frames in Hilbert spaces. We begin by establishing a comprehensive framework for the MRC, emphasizing its importance in ensuring…
The second-order, small-scale dependence structure of a stochastic process defined in the space-time domain is key to prediction (or kriging). While great efforts have been dedicated to developing models for cases in which the spatial…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
Part I of the paper considered infinite orthogonal sums of regular subspaces in a Krein space (that is, of subspaces which are themselves Krein spaces). How precisely these sums should be defined and conditions for when such a sum is itself…