Related papers: Modular Biframes for Operators
We study multiview moduli problems that arise in computer vision. We show that these moduli spaces are always smooth and irreducible, in both the calibrated and uncalibrated cases, for any number of views. We also show that these moduli…
The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of…
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs.…
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…
A general invariant manifold theorem is needed to study the topological classes of smooth dynamical systems. These classes are often invariant under renormalization. The classical invariant manifold theorem cannot be applied, because the…
We define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Because of this…
This is an expository-survey on weak stability of bounded linear operators acting on normed spaces in general and, in particular, on Hilbert spaces. The paper gives a comprehensive account of the problem of weak operator stability,…
Compositionality is a key strategy for addressing combinatorial complexity and the curse of dimensionality. Recent work has shown that compositional solutions can be learned and offer substantial gains across a variety of domains, including…
We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.
Supersymmetry might be broken, in the real world, by anomalies that affect composite operators, while leaving the action supersymmetric. New constraint equations that govern the composite operators and their anomalies are examined. It is…
We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…
The main purpose is to introduce the so-called bicomplex (bc)-frames which is a special extension to bicomplex infinite Hilbert spaces of the classical frames. The crucial result is the characterization of bc-frames in terms of their…
Using the matrix representation of Fourier integral operators with respect to a Gabor frame, we study their compactness on weighted modulation spaces. As a consequence, we recover and improve some compactness results for pseudodifferential…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Deformable object manipulation (DOM) is an emerging research problem in robotics. The ability to manipulate deformable objects endows robots with higher autonomy and promises new applications in the industrial, services, and healthcare…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…