bio | website | math.umn.edu/~garrett |
---|---|---|
location | US | |
age | 62 | |
visits | member for | 3 years, 6 months |
seen | 1 hour ago | |
stats | profile views | 4,675 |
I am interested in the application of modern analysis to the spectral theory of Eisenstein series and other automorphic forms, L-functions, and number theory. This includes representation theory of (mostly reductive) Lie groups and p-adic 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.
Oct 15 |
comment |
Source needed (at final-year undergrad level) for the double cover of SO(3) by SU(2)
@JoelFine and Jose'F.-O'F, it seems to me very funny that at this moment in history quaternions could conceivably be "less elementary" than Lie algebras (although, I hasten to add, I am a very great fan of Lie algebras, etc, etc, etc, ...!!!) Pity that this example of-so-many-things has become obscure... |
Oct 14 |
comment |
Oddify an even function and vice versa: need a Fourier transform-based formula
My reason for asking is that I (and maybe others) can only guess what features of the code are essential for your purposes, and what are artifactual. |
Oct 14 |
comment |
Oddify an even function and vice versa: need a Fourier transform-based formula
It might be good to tell what characterization of the "corresponding odd/even part" you have/want. With no constraints, this would be completely ambiguous. In the mathematica code [sic] this is a tacit characterization, but could you amplify on your goals? |
Oct 14 |
comment |
Has uniform ellipticity implications on the spectrum?
Isn't the usual Laplacian on $\mathbb R^n$ "uniformly elliptic", but with purely continuous spectrum? |
Oct 14 |
reviewed | Close Squares sum problem |
Oct 11 |
comment |
Non invertibility of certain integral arising from group action
Ah, ok, in light of your edits, I'll remove my earlier comments in a little while... |
Oct 10 |
answered | The periodic architecture underlying the natural numbers |
Oct 9 |
reviewed | Close Why is the order of the difference operator defined as $p$ rather than $p+1$ for the second order differential equation? |
Oct 9 |
reviewed | Close Largest eigenvalue of the sum of hermitian matricies |
Oct 7 |
comment |
on the Rankin-Selberg L-function
Yes, I'd be entirely willing to believe that there is some delicacy in that situation... |
Oct 7 |
comment |
on the Rankin-Selberg L-function
With cuspidal data and $m\not=n$ it is relatively straightforward to prove that there is no pole in the right half-plane from the critical line. For $m=n-1$ the form of the integral representation (the "Hecke" form) also makes clear that the $L$-function is entire, for cuspidal data. For $m=n$ but non-contragredient cuspidal data, again the form of the integral repn makes clear the entire-ness. All other cases are more complicated... |
Oct 6 |
revised |
Fourier approximation error in L^2 for piecewise continuous functions
edited body |
Oct 6 |
answered | Fourier approximation error in L^2 for piecewise continuous functions |
Oct 5 |
answered | Inequality for a gamma function |
Oct 2 |
revised |
algebraic groups over non-archimedean local fields acting on buildings
edited tags; edited tags |
Oct 2 |
answered | algebraic groups over non-archimedean local fields acting on buildings |
Oct 1 |
answered | On the reductive group |
Sep 28 |
comment |
Who first showed that $SL(n,O_K)$ is a lattice for a number ring $O_K$?
Hilbert's student Blumenthal treated examples of this for $SL_2$ very early in the 20th century, to study Hilbert-Blumenthal modular forms. Siegel's arguments of the 1930s and 1940s for computing volumes of the quotients attached to $SL_n(\mathbb Z)$ and $Sp_n(\mathbb Z)$ immediately apply to number fields, imitating some aspects of Hecke's 1910s and 1920s treatments of $L$-functions attached to number fields. |
Sep 28 |
revised |
Topology on the space of Schwartz Distributions
added 852 characters in body |
Sep 22 |
comment |
What justification can you give for the fact that “most ODEs do not have an explicit solution”?
As is often the case, "explicit" is a misnomer for "elementary", where the latter more literally refers to polynomials, exponentials-and-logs, trig functions, roots, ... As in is implicit in Loic Teyssier's answer, the coefficients of a differential equation can be elementary, while the solutions are demonstrably not. |