bio  website  math.umn.edu/~garrett 

location  US  
age  63  
visits  member for  4 years, 3 months 
seen  45 mins ago  
stats  profile views  5,309 
I am interested in the application of modern analysis to the spectral theory of Eisenstein series and other automorphic forms, Lfunctions, and number theory. This includes representation theory of (mostly reductive) Lie groups and padic groups, and harmonic analysis on these groups and their homogeneous spaces. Necessarily Schwartz' distributions, Sobolev spaces, and similar things play important supporting roles. I find that a mildly categorical viewpoint is very helpful in keeping things straight.
2d

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History of Geometric Analogies in Number Theory
I think that Minkowski's "geometry of numbers" is not the sense of the question, which is more about the analogies between rings of algebraic integers and integral extensions of $\mathbb F_q[T]$. 
Jul 1 
answered  Are spherical harmonics uniformly bounded? 
Jun 23 
comment 
Uniform convergence of Fourier (orthonormal) expansion of series
I don't know about a definitive result for "pointwise a.e." convergence in higher dimensions. But/and such a result by itself (even as difficult as the Carleson result is in one dimension) doesn't allow us to do much with the expansion without further hypotheses (hence, my mentioning uniform pointwise and Sobolev imbedding sortsofthings). 
Jun 22 
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When does analytic in the operator norm imply analytic in the trace class norm?
I'm sorry, I didn't mean to suggest that tracenorm continuity implies operator analyticity. Maybe I misunderstood what hypothesis you're taking and hoping to prove tracenorm analyticity... 
Jun 22 
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When does analytic in the operator norm imply analytic in the trace class norm?
I'm confused by your opening remarks: if you've proven that continuity of $W(\lambda)$ in operator norm implies holomorphy in trace norm, then since that continuity is implied by analyticity in the operator norm, you'd be done... ? Is there a typo? Am I misunderstanding something? 
Jun 22 
answered  Uniform convergence of Fourier (orthonormal) expansion of series 
Jun 21 
revised 
Spherical harmonics and ellipticity of the Laplacian
added 13 characters in body 
Jun 21 
reviewed  Leave Open $\mathbb{P}_{\kappa}$ forces non$(\mathcal{M})$=cov$(\mathcal{M})=\kappa$ 
Jun 21 
reviewed  Close example of non computable implicit operations 
Jun 21 
reviewed  Leave Open Representation Theory of $U(N)$ 
Jun 20 
answered  Spherical harmonics and ellipticity of the Laplacian 
Jun 19 
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Does there exist a smooth version of Cohen's factorization theorem?
Not clear to me, either. The argument is not at all trivial, even after Casselman's discussion... Entire functions and such... 
Jun 19 
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Does there exist a smooth version of Cohen's factorization theorem?
I don't really know about the latest on this. Bill Casselman has a nice essay about DM and its proof on his website ... which probably you can find as quickly as I can. :) 
Jun 19 
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Does there exist a smooth version of Cohen's factorization theorem?
It's not only approximated, but equal. (The weaker and much easier "approximation" assertion is essentially Garding's from 1947 or so, which would also cope directly with approximation of smooth by convolutions). But then, in any case, you can certainly approximate arbitrary smooth by test functions, if that's enough for you. To get exact equality with $C^\infty*C^\infty_c$ seems tricky... Is approximation good enough for you? 
Jun 19 
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Does there exist a smooth version of Cohen's factorization theorem?
So the DM result is not addressing some aspect of things relevant to your purposes? Yes, the DM more directly addresses test functions, i.e., compactlysupported, not all smooth, but that's not a fatal problem. A technical point is that finite sums are necessary in that context, so not every test function is exactly a single convolution of two. Can you clarify your issue? 
Jun 19 
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Does there exist a smooth version of Cohen's factorization theorem?
Isn't this exactly the DixmierMalliavin result? 
Jun 19 
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different definitions of epsilon constants for representations of GL(2) from modular forms
If it's any consolation, I think that the issue of the compatibilities of various notions of epsilonfactor are not easy to certify. I seem to recall reading that Dwork and Langlands and others decided to not publish (!?!) certain of their investigations into such compatibilities because the writeup would simply "go on too long". In particular, any arrangement of an argument that would show that almostall local epsilons are $1$, and certify the notion that a global epsilonfactor is welldefined, and so on, is apparently ... expensive. 
Jun 17 
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Fourier series and transform related to Epicycles
The context confuses me, even if it confuses no one else: a "curve" as posed is exactly a complexvalued function on the circle, so certainly has a (complexvalued) Fourier series, and these things have been studied for a long time. I'd think that imbedding it in that context, or at least talking in a way that allows reference to it, would help people answer usefully... 
Jun 13 
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Fourier expansion of Eisenstein Series
Your link to Zagier's paper is slightly mangled: it should have mpimbonn rather than mpimbonn... 
Jun 9 
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padic asymptotic analysis
I do not know of any intro on this... but/and, having thought about the archimedean case (!?!) in recent years, I wonder what things you're wanting... 