Allometry constants of finite-dimensional spaces: theory and computations |
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Authors: | Simon Foucart |
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Institution: | (1) Vanderbilt University, Nashville, TN 37240, USA |
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Abstract: | We describe the computations of some intrinsic constants associated to an n-dimensional normed space , namely the N-th “allometry” constants
These are related to Banach–Mazur distances and to several types of projection constants. We also present the results of our
computations for some low-dimensional spaces such as sequence spaces, polynomial spaces, and polygonal spaces. An eye is kept
on the optimal operators T and T′, or equivalently, in the case N = n, on the best conditioned bases. In particular, we uncover that the best conditioned bases of quadratic polynomials are not
symmetric, and that the Lagrange bases at equidistant nodes are best conditioned in the spaces of trigonometric polynomials
of degree at most one and two. |
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Keywords: | Condition numbers Banach– Mazur distances Projection constants Extreme points Frames |
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