Concrete constructions of non-pavable projections
Peter G. Casazza, Matt Fickus, Dustin Mixon, Janet C. Tremain
TL;DR
This paper provides explicit examples of non-pavable projections with constant diagonal entries, advancing understanding of the paving conjecture's limitations.
Contribution
It constructs concrete examples of non-pavable projections with constant diagonals, moving beyond existence proofs.
Findings
Explicit examples of non-pavable projections with diagonal 1/2
Examples of projections with diagonal 1/r that are not r-pavable
Strengthening the understanding of the paving conjecture's boundaries
Abstract
It is known that the paving conjecture fails for 2-paving projections with constant diagonal 1/2. But the proofs of this fact are existence proofs. We will give concrete examples of these projections and projections with constant diagonal which are not -pavable in a very strong sense.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Numerical Analysis Techniques · Algebraic and Geometric Analysis