相关论文: On Cantor's singular moments
In the article 'Ordinal Logics and the Characterizations of the Informal Concept of Proof', Georg Kreisel poses the problem of assigning unique notations to recursive ordinals, and additionally suggests that the methods which are developed…
Linear non-compact operators are difficult to study because they do not exist in the finite dimensional world. Recently, Math\'{e} and Hofmann studied the singular values of the compact composition of the non-compact Hausdorff moment…
We consider a class of singular weighted anisotropic $p$-Laplace equations. We provide sufficient condition on the weight function that may vanish or blow up near the origin to ensure the existence of at least one weak solution in the…
Any careful singularity analysis of the Mixmaster Universe uncovers the instance of a triple -1 resonance. The Mixmaster Universe does not exhibit a closed-form solution and so a correct interpretation of the meaning of the triple -1…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
This paper is devoted to the construction of weak solutions to the singular constant $Q$-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of…
Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is…
We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all…
In this paper we classify the isolated singularities of positive solutions to Choquard equation and prove the existence of isolated singular solutions.
We present an algorithm for computing instanton numbers of curve singularities. A comparison is made between these and some other invariants of curve singularities. The algorithm has been implemented in the symbolic computer algebra program…
A 1910 theorem of Brouwer characterizes the Cantor set as the unique totally disconnected, compact metric space without isolated points. A 1920 theorem of Sierpinski characterizes the rationals as the unique countable metric space without…
In 1891 Cantor presented two proofs with the purpose to establish a general theorem that any set can be replaced by a set of greater power. Cantor's power set theorem can be considered to be an extension of Cantor's 1891 second proof and…
We show that the possible Cantor-Bendixson ranks of countable SFTs are exactly the finite ordinals and ordinals of the form $\lambda + 3$, where $\lambda$ is a computable ordinal. This result was claimed by the author in his PhD…
The question of whether it is possible to compute scattering resonances of Schr\"odinger operators - independently of the particular potential - is addressed. A positive answer is given, and it is shown that the only information required to…
The present article is devoted to representations of rational numbers in terms sign-variable Cantor expansions. The main attention is given to one of the discussions given by J. Galambos in [4].
The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…
We consider Cantor measures on the line, with contraction factor $N^{-1}=p^{-\alpha}$ (where $p$ a positive prime, $\alpha$ a positive integer) and $m$ positive integer digits lying in distinct residue classes modulo $N$. We obtain a…
he Singular Manifold Method is presented as an excellent tool to study a 2+1 dimensional equation in despite of the fact that the same method presents several problems when applied to 1+1 reductions of the same equation. Nevertheless these…
In this paper, we consider the rank-one tensor completion problem. We address the question of existence and uniqueness of the rank-one solution. In particular we show that the global uniqueness over the field of real numbers can be verified…
In this article we give necessary and sufficient conditions that a complex number must satisfy to be a continuous eigenvalue of a minimal Cantor system. Similarly, for minimal Cantor systems of finite rank, we provide necessary and…