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location University of Maryland
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seen Mar 7 at 19:32

I am a PhD student at the University of Maryland working on tilings and their relationship to harmonic analysis.


Jan
14
revised Is any finite collection of points contained in a cut and project set with $\mathbb{R}^d$ as internal space?
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Jan
14
asked Is any finite collection of points contained in a cut and project set with $\mathbb{R}^d$ as internal space?
Dec
20
comment When is a collection of exponentials dense in $L^2(K), |K|<\infty$
This book seems concentrated on the $d=1$ case. Has a similar analysis been done in higher dimensions?
Dec
20
awarded  Critic
Dec
20
comment When is a collection of exponentials dense in $L^2(K), |K|<\infty$
Ah thanks. Are there particular techniques for proving that a set is a set of uniqueness?
Dec
20
revised When is a collection of exponentials dense in $L^2(K), |K|<\infty$
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Dec
20
comment When is a collection of exponentials dense in $L^2(K), |K|<\infty$
Yes, I meant to ask when the linear span of the set $\{e^{2 \pi i \lambda}\}$ would be dense. Certainly the Paley-Wiener theorem relates $L^2(K)$ to holomorphic functions with certain growth conditions. What do you mean by a "set of uniqueness?"
Dec
20
revised When is a collection of exponentials dense in $L^2(K), |K|<\infty$
added 7 characters in body
Dec
20
comment When is a collection of exponentials dense in $L^2(K), |K|<\infty$
I'll amend the question to specify that $K$ should be compact.
Dec
20
comment When is a collection of exponentials dense in $L^2(K), |K|<\infty$
Thanks! I am especially interested in the question for $K \subset \mathbb{R}^d, d>1.$
Dec
20
asked When is a collection of exponentials dense in $L^2(K), |K|<\infty$
Dec
17
answered Finding the commutant of a von Neumann algebra
Nov
26
comment Finding the commutant of a von Neumann algebra
Thank you for your answer! Indeed, the algebras I am dealing with are Type II factors acting on B(L^2(X)) where X is a topological space. Is there some classification of the operators on B(L^2(X)) that would allow me to systematically check that the operators in B are the only ones commuting withoperators in A (or vice versa)?
Nov
25
asked Finding the commutant of a von Neumann algebra
Oct
28
revised The groupoid VN algebra of the transversal to a uniquely ergodic action
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Oct
15
revised The groupoid VN algebra of the transversal to a uniquely ergodic action
edited tags
Oct
10
revised The groupoid VN algebra of the transversal to a uniquely ergodic action
added 186 characters in body
Oct
10
asked The groupoid VN algebra of the transversal to a uniquely ergodic action
Oct
2
comment Poisson Summation Formulas for Cut and Project Quasicrystals
I imagine a similar argument can be used to show that patches in the tiling space occur with uniform frequencies (and to compute those frequencies). Would you happen to know of a reference with those sorts of computations? I've seen things like this in a paper of Solomyak, but it was for self-affine tilings rather than cut and projects.
Oct
2
comment Poisson Summation Formulas for Cut and Project Quasicrystals
What are the $A_n$ in the limit?