DML-PL - Yadda

1

Interpolation Gevrey dans les domaines de type fini de $ℂ^2$

100%

Thilliez V.

Banach Center Publications

|

1995

|

tom 31

|

nr 1

359-365

2

Extension Gevrey et rigidité dans un secteur

100%

Thilliez V.

Studia Mathematica

|

1995-1996

|

tom 117

|

nr 1

29-41

EN

We study a rigidity property, at the vertex of some plane sector, for Gevrey classes of holomorphic functions in the sector. For this purpose, we prove a linear continuous version of Borel-Ritt's theorem with Gevrey conditions

3

Łojasiewicz ideals in Denjoy-Carleman classes

100%

Thilliez V.

Studia Mathematica

|

2013

|

tom 216

|

nr 1

35-46

EN

The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the $𝓒^{∞}$ case have a Denjoy-Carleman counterpart.

4

Division et extension dans des classes de Carleman de fonctions holomorphes

100%

Thilliez V.

Banach Center Publications

|

1998

|

tom 44

|

nr 1

233-246

EN

Let Ω be a bounded pseudoconvex domain in $ℂ^n$ with $C^1$ boundary and let X be a complete intersection submanifold of Ω, defined by holomorphic functions $v_1,...,v_p$ (1 ≤ p ≤ n-1) smooth up to ∂Ω. We give sufficient conditions ensuring that a function f holomorphic in X (resp. in Ω, vanishing on X), and smooth up to the boundary, extends to a function g holomorphic in Ω and belonging to a given strongly non-quasianalytic Carleman class ${l!M_l}$ in $\bar Ω$ (resp. satisfies $f = v_1 f_1+... + v_p f_p$ with $f_1,...,f_p$ holomorphic in Ω and ${l!M_l}$-regular in $\bar Ω$). The essential assumption is that f and $v_1,... ,v_p$ belong to some (maybe smaller) Carleman class ${l!M^-_l}$, where the sequences $M^-$ and M are precisely related by geometric conditions on X and Ω.

5

Bounds for quotients in rings of formal power series with growth constraints

100%

Thilliez V.

Studia Mathematica

|

2002

|

tom 151

|

nr 1

49-65

EN

In rings $Γ_{M}$ of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence $M = (M_{l})_{l≥0}$ (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in $Γ_{M}$ such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to $Γ_{M}$, provided $Γ_{M}$ is stable under derivation. By a further development of the method, we obtain the main result of the paper, stating that the ideals generated by a given analytic germ in rings of ultradifferentiable germs are closed provided the generator is homogeneous and has an isolated singularity in ℝⁿ. The result is valid under the aforementioned assumption of stability under derivation, and it does not involve (non-)quasianalyticity properties.

6

Prolongement dans des classes ultradifférentiables et propriétés de régularité des compacts de $ℝ^n$

100%

Thilliez V.

Annales Polonici Mathematici

|

1996

|

tom 63

|

nr 1

71-88

EN

Considering jets, or functions, belonging to some strongly non-quasianalytic Carleman class on compact subsets of $ℝ^n$, we extend them to the whole space with a loss of Carleman regularity. This loss is related to geometric conditions refining Łojasiewicz's "regular separation" or Whitney's "property (P)".

Ograniczanie wyników

3 Studia Mathematica

2 Banach Center Publications

1 Annales Polonici Mathematici

6 Thilliez V.

1 2013

1 2002

1 1998

1 1996

2 1995

Wyniki wyszukiwania

Interpolation Gevrey dans les domaines de type fini de $ℂ^2$

Extension Gevrey et rigidité dans un secteur

Łojasiewicz ideals in Denjoy-Carleman classes

Division et extension dans des classes de Carleman de fonctions holomorphes

Bounds for quotients in rings of formal power series with growth constraints

Prolongement dans des classes ultradifférentiables et propriétés de régularité des compacts de $ℝ^n$