相关论文: About Stability of Irreducibility for Germs of Hol…

We study the action of irreducible derivations X on some Hilbert's quasi-regular algebras QRH of germes at 0 of analytic functions on (U,0), where U is a semi-algebraic set: that is, we show that these algebras are X-finite or locally…

Using nonstandard analysis we define a topology on the ring of germs of functions: $(mathbb R^n,0)\rightarrow(mathbb R,0)$. We prove that this topology is absolutely convex, Hausdorff, that convergent nets of continuous germs have…

The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous…

Let k be an algebraically closed field of characteristic zero. An element F from k(x_1,...,x_n) is called a closed rational function if the subfield k(F) is algebraically closed in the field k(x_1,...,x_n). We prove that a rational function…

It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…

Let $F$ be a local field of characteristic $p$ and $G$ be a connected reductive group over $F$. Recall that Shalika's germ expansion of orbital integrals of regular semi-simple elements near the identity, when it exists, is a sum indexed by…

We study conditions on closed sets $C,F \subset \mathbb{R}$ making the product $C \times F$ removable or non-removable for $W^{1,p}$. The main results show that the Hausdorff-dimension of the smaller dimensional component $C$ determines a…

For an analytic family P_s of polynomials in n variables (depending on a complex number s, and defined in a neighborhood of s = 0), there is defined a monodromy transformation h of the zero level set V_s= {P_s=0} for s different from 0,…

The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…

We give complete and exact descriptions of spaces of ultradifferentiable functions that are closed under composition with either holomorphic or ultradifferentiable functions -- which are two distinct cases. The proof works by considering…

The character of an irreducible admissible representation of a $p$-adic reductive group is known to be a constant function in some neighborhood of any regular semisimple element $\gamma$ in the group. Under certain mild restrictions on…

Let D be a bounded, finitely connected domain in the complex plane without isolated points in the boundary and let f be a continuous function on the boundary bD. Let F be a continuous extension of f to the closure of D. We prove that f…

In this paper, we establish the following criterion for divisibility in the local ring of those quasianalytic function germs at zero which are definable in a polynomially bounded structure. A sufficient (and necessary) condition for the…

We prove that the linearization of a germ of holomorphic map of the type $F_\lambda(z)=\lambda(z+O(z^2))$ has a $ C^1$--holomorphic dependence on the multiplier $\lambda$. $C^1$--holomorphic functions are $ C^1$--Whitney smooth functions,…

A well-known theorem due to Ma\~n\'e-Sad-Sullivan and Lyubich asserts that J-stable maps are dense in any holomorphic family of rational maps in dimension 1. In this paper we show that the corresponding result fails in higher dimension.…

Let $M$ be a subharmonic function with Riesz measure $\nu_M$ in a domain $D$ in the $n$-dimensional complex Euclidean space $\mathbb C^n$, and let $f$ be a nonzero function that is holomorphic in $D$, vanishes on a set ${\sf Z}\subset D$,…

Let $f$ be a germ of holomorphic diffeomorphism of $\C^n$ fixing the origin $O$, with $df_O$ diagonalizable. We prove that, under certain arithmetic conditions on the eigenvalues of $df_O$ and some restrictions on the resonances, $f$ is…

We consider diffeomorphisms $f$ with heteroclinic cycles associated to saddles $P$ and $Q$ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to $f$ with a robust cycle associated to…

If $V$ is an analytic set in a pseudoconvex domain $\Omega$, we show there is always a pseudoconvex domain $G \subseteq \Omega$ that contains $V$ and has the property that every bounded holomorphic function on $V$ extends to a bounded…

We present a rigidity property of holomorphic generators on the open unit ball $\mathbb{B}$ of a Hilbert space $H$. Namely, if $f\in\Hol (\mathbb{B},H)$ is the generator of a one-parameter continuous semigroup ${F_t}_{t\geq 0}$ on…