Abstract
AbstractIn this note we consider the nonlinear heat equation associated to the fractional Hermite operator $$H^\beta =(-\Delta +|x|^2)^\beta $$
H
β
=
(
-
Δ
+
|
x
|
2
)
β
, $$0<\beta \le 1$$
0
<
β
≤
1
. We show the local solvability of the related Cauchy problem in the framework of modulation spaces. The result is obtained by combining tools from microlocal and time-frequency analysis. As a byproduct, we compute the Gabor matrix of pseudodifferential operators with symbols in the Hörmander class $$S^m_{0,0}$$
S
0
,
0
m
, $$m\in \mathbb {R}$$
m
∈
R
.
Funder
Università degli Studi di Torino
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
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