Related papers: A converse of Cartan's Theorem B for Real Analytic…

In 1957 Cartan proved his celebrated Theorem B and deduced that if $\Omega\subset{\mathbb R}^n$ is an open set and $X$ is a coherent real analytic subset of $\Omega$, then $X$ has the analytic extension property: Each real analytic function…

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

We prove a converse theorem for split even special orthogonal groups over finite fields. This is the only case left on converse theorems of split classical groups and the difficulty is the existence of the outer automorphism. In this paper,…

There has been a recent coming together of the Converse Theorem for $\gln$ and the Langlands-Shahidi method of controlling the analytic properties of automorphic $L$-functions which has allowed us to establish a number of new cases of…

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

In this paper, we prove a converse theorem for half-integral weight modular forms assuming functional equations for $L$-series with additive twists. This result is an extension of Booker, Farmer, and Lee's result in [BFL22] to the…

The Baer theorem states that for a group $G$ finiteness of $G/Z_i(G)$ implies finiteness of $\gamma_{i+1}(G)$. In this paper we show that if $G/Z(G)$ is finitely generated then the converse is true.

The converse of Fortin's Lemma in Banach spaces is established in this Note.

The Holant theorem is a powerful tool for studying the computational complexity of counting problems in the Holant framework. Due to the great expressiveness of the Holant framework, a converse to the Holant theorem would itself be a very…

We prove the converse of Yano's extrapolation theorem for translation invariant operators.

We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.

We prove an analytic Bertini theorem, generalizing a previous result of Fujino and Matsumura.

We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.

In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.

In this paper, we completely prove a standard conjecture on the local converse theorem for generic representations of GLn(F), where F is a non-archimedean local field.

The balayage of a Carleson measure lies of course in BMO. We show that the converse statement is false. We also make a two-sided estimate of the Carleson norm of a positive measure in terms of balayages.

We give a new proof of a classical theorem on approximation of continuous functions on totally real sets

This is an expanded version of the author's lecture at the XX Congresso U.M.I., held in Siena in September 2015. After a brief review of L-functions, we turn to the classical converse theorems of H.Hamburger, E.Hecke and A.Weil, and to some…

The possibility of reversion of the inequality in the Second Main Theorem of Cartan in the theory of holomorphic curves in projective space is discussed. A new version of this theorem is proved that becomes an asymptotic equality for a…

On any torus $\mathbb{T}^d$, $d \geq 2$, we prove the existence of a real-analytic diffeomorphism $T$ with a good approximation of type $\left(h,h+1\right)$, a maximal spectral type disjoint with its convolutions and a homogeneous spectrum…