The minimizers of the p-frame potential
WebFrame theory generalizes the idea of bases in Hilbert space, and the frame potential is an important tool when studying frame theory. In this thesis, we first explore the minimization problem of a generalized definition of frame potential, namely the p-frame potential, and show there exists a universal optimizer under certain conditions by applying a method … WebOne of our main results establishes the unique minimizer for big enough p. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the p -frame potential. We conclude the paper by reporting some numerical experiments for the case d ≥ 3, N = d + 1, and p ∈ (0,2).
The minimizers of the p-frame potential
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Web8 P.G. Casazza, M. Fickus Generally speaking, frame theory is the study of how {f m}M m=1 should be chosen in order to guarantee that F∗F is well-conditioned. In particular, {fm}M m=1 is a frame for H N if there exists frame bounds 0 Webdecision makers adopting different frames for their decisions. Frames refer to the decision maker’s conception of the acts, outcomes, and contingencies associated with a particular choice. The adoption of a given frame depends not only on the personal characteristics of the decision maker, but also on the formulation of the problem itself.
Webinteger values of p.Wheneverp 2 2N,thep-frame energy is minimized by the normalized surface measure [Si, EO], among other measures. However, for p 622N, all the minimizers appear to be discrete [BGM+]. For p = 2, this energy and its discrete counterpart, often referred to simply as the frame potential,havebeenstudiedin[Si] and later again in ... Webframes with speci ed symmetries be characterized as local minimizers of the frame potential? Example 1.4. Let != e2ˇi=3 and de ne Ato be the 2 2 matrix A= ! 0 0 !2 : Given u2C2 with kuk= 1, consider the collection X = fAjug2 j=0. It will be shown that the local minimizers of the frame potential of X(under the constraint
WebFeb 9, 2024 · unique minimizer for big enough $p$. Moreover, this minimizer is universal in the sense that it minimizes a large range of energy functions that includes the $p$-frame potential. We conclude the paper by reporting some numerical experiments for the case $d\geq 3$, $N=d+1$, $p\in (0, 2)$. These experiments lead to some conjectures that we …
Web8 rows · May 1, 2024 · The aim of this paper is to confirm Conjecture 1.1 and to show that the minimizers are unique ... In this paper, we focus on this quantity for N = d + 1 points and establish uniqueness … Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary … We introduce a numerical measure of how well a frame reconstructs vectors when … Indeed, take 2 vectors of length ^"\/6 in opposite directions along each axis of an … Positive definite kernels on homogeneous spaces and certain stochastic processes … We first use Theorem 2.2 to characterize the minimizers of the p-frame potential … m\u0026s womens party dressesWebMar 3, 2024 · It consists of 10 statements and identified 3 patient groups - minimizers, moderate maximizers and strong maximizers. Medical maximizers (people scoring highly on the MMS) prefer to receive more health care visits, medications, tests, and treatments, whereas minimizers prefer fewer services. m\u0026s womens long sleeve t shirtsWebMar 16, 2024 · The shock collapse of Silicon Valley Bank has erupted in a volley of finger pointing at central banks, regulators, venture capitalists and governments. However, this is only part of the story. Until we understand the cyclical nature of financial crises, and take a step back to contextualise our current situation, we will always be on the back foot when … how to make taming foodWebWe also prove that for 1 ≤ m < d, a repeated orthonormal basis construction of N = d + m vectors minimizes the energy over an interval, p ∈ [ 1, p m], and demonstrates an … m\u0026s womens thermal wearWebFeb 9, 2024 · For the special case p=2 and p=∞, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals FP_p, N, d, by first establishing some general properties of their minima. ... The definition of the p-frame potential above differs from the one given in … m\u0026s womens sleeveless cashmere knitWebApr 7, 2024 · このサイトではarxivの論文のうち、30ページ以下でCreative Commonsライセンス（CC 0, CC BY, CC BY-SA）の論文を日本語訳しています。 how to make tamarind seed powderWebMar 1, 2012 · We first use Theorem 2.2 to characterize the minimizers of the p-frame potential for 0 < p < 2 provided that the number of points N is a multiple of the dimension d: Theorem 3.5. Let 0 < p < 2 and assume that N=kd for some positive integer k. Then the minimizers of the p-frame potential are exactly the k copies of any orthonormal basis … m \u0026 s womens padded coats