2006
DOI: 10.1016/j.jfa.2005.12.017
|View full text |Cite
|
Sign up to set email alerts
|

Super-exponential decay and holomorphic extensions for semilinear equations with polynomial coefficients

Abstract: We show that all eigenfunctions of linear partial differential operators in $R^n$ with polynomial coefficients. We also show that under semilinear\ud polynomial perturbations all nonzero homoclinics keep the super-exponential decay of the above type,\ud whereas a loss of the holomorphicity occurs. Our estimates on homoclinics are sharp.\ud of Shubin type are extended to entire functions in $C^n$ of finite exponential type 2 and decay like $exp(−|z|2)$\ud for $|z|\to \infty$ in conic neighbourhoods of the form … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

2
32
0

Year Published

2009
2009
2019
2019

Publication Types

Select...
5
3

Relationship

2
6

Authors

Journals

citations
Cited by 34 publications
(34 citation statements)
references
References 22 publications
2
32
0
Order By: Relevance
“…As a corollary, we recover a result first observed in [2]: If P is globally elliptic then all its eigenfunctions belong to…”
Section: ) In the Beurling Case We Obtainsupporting
confidence: 84%
See 1 more Smart Citation
“…As a corollary, we recover a result first observed in [2]: If P is globally elliptic then all its eigenfunctions belong to…”
Section: ) In the Beurling Case We Obtainsupporting
confidence: 84%
“…In this section we exploit the iterative approach from [2,9,18] in order to obtain a structural characterization of S * (R n ) in terms of the growth of the L 2 norms of the iterates of the operator P . The regularity result Theorem 1.2 will readily follow from Theorem 3.4 below.…”
Section: Iterates Of the Operator And Regularity Of Solutionsmentioning
confidence: 99%
“…provided (1.4) holds; see [3], [4] for details and more general results. We assume, as in Seeley [16], that P is a normal operator (i.e., P * P = P P * ) satisfying the global ellipticity condition (1.4).…”
Section: Introduction and Statement Of The Resultsmentioning
confidence: 99%
“…The other standard way is to use Theorem 25.4 (with m = m 0 = 2) in [16], which implies that 4) and using appropriate mapping properties of pseudo-differential operators with symbols satisfying (0.4). In [3] more refined estimates are established for the solutions f ∈ S ′ (R d ) of the equation Hf = g and for more general differential operators when g belongs to the GelfandShilov space S s (R d ), s ≥ 1/2 (cf. Section 1 for the definitions).…”
Section: Introductionmentioning
confidence: 99%
“…Theorem 2.1, Proposition 2.2 ′ and Remarks 2.4 and 2.5). Starting from the estimate (0.6) for b d , it might be interesting to study general symbols satisfying estimates of the same type and to establish regularity results for the related operators in the setting of Gelfand-Shilov spaces as it has been done in [3][4][5]. We will treat these applications in future papers and focus here only on the model H −1 .…”
Section: Introductionmentioning
confidence: 99%