Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An estimate for spherical functions on $\mathrm{SL}(3,\mathbb{R})$   We prove an estimate for spherical functions $\phi_\lambda(a)$ on
$\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral
parameter $\lambda$ when the group parameter $a$ is restricted to a compact
subset of the abelian subgroup $\mathrm{A}$. In the case of
$\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C.
Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain
regular. As in their work, we estimate the oscillatory integral that appears in
the integral formula for spherical functions by the method of stationary phase.
However, the major difference is that we investigate the stability of the
singularities arising from the linearized phase function by classifying their
local normal forms when the parameters $\lambda$ and $a$ vary.

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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th