» On curve-flat Lipschitz functions and their linearizations
14/11/24 10:00 from math.FA updates on arXiv.org
arXiv:2411.08369v1 Announce Type: new Abstract: We show that several operator ideals coincide when intersected with the class of linearizations of Lipschitz maps. In particular, we show that the linearization $\hat{f}$ of a Lipschitz map...

» Exact Eigenvalues and Eigenvectors for Some n-Dimensional Matrices
14/11/24 10:00 from math.SP updates on arXiv.org
arXiv:2411.08239v1 Announce Type: new Abstract: Building on previous work that provided analytical solutions to generalised matrix eigenvalue problems arising from numerical discretisations, this paper develops exact eigenvalues and eige...

» On wavelet coorbit spaces associated to different dilation groups
14/11/24 10:00 from math.FA updates on arXiv.org
arXiv:2411.08416v1 Announce Type: new Abstract: This paper develops methods based on coarse geometry for the comparison of wavelet coorbit spaces defined by different dilation groups, with emphasis on establishing a unified approach to b...

» Application of Operator Theory for the Collatz Conjecture
14/11/24 10:00 from math.OA updates on arXiv.org
arXiv:2411.08084v1 Announce Type: new Abstract: In this paper, we formulate the Collatz conjecture (or the $3n{+}1$-problem) as some operator theoretic problems and prove that each of those statements is equivalent to the conjecture.

» Coexistence of Hilbert space effects and orthogonality
14/11/24 10:00 from math.FA updates on arXiv.org
arXiv:2411.08445v1 Announce Type: new Abstract: In this paper, we show that every pair of absolutely compatible Hilbert space effects are coexistent and exhibit a partial orthogonality property. We introduce the notion of partially ortho...

» New matrices for spectral hypergraph theory, II
14/11/24 10:00 from math.SP updates on arXiv.org
arXiv:2411.08137v1 Announce Type: cross Abstract: The properties of a hypergraph explored through the spectrum of its unified matrix was made by the authors in [26]. In this paper, we introduce three different hypergraph matrices: unifie...

» Hilbert space embeddings of independence tests of several variables
14/11/24 10:00 from math.FA updates on arXiv.org
arXiv:2411.08653v1 Announce Type: new Abstract: In this paper, we present the general theory of embedding independence tests on Hilbert spaces that generalizes the concepts of distance covariance, distance multivariance and HSIC. This is...

» Semiclassical measure of the spherical harmonics by Bourgain on $\mathbb{S}^3$
14/11/24 10:00 from math.SP updates on arXiv.org
arXiv:2411.08146v1 Announce Type: cross Abstract: Bourgain used the Rudin-Shapiro sequences to construct a basis of uniformly bounded holomorphic functions on the unit sphere in $\mathbb{C}^2$. They are also spherical harmonics (i.e., La...

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