Related papers: Differentiability Properties of Log-Analytic Funct…
Let M be a real analytic manifold, F a bounded complex of constructible sheaves. We show that the Whitney-de Rham complex associated to F is quasi-isomorphic to F.
We study functions defined on a closed segment of the real line that belong to the class of Gonchar. We show that the graphs of such functions are pluripolar. We also discuss the generalizations of our result to functions defined on a…
In this note we provide explicit expressions and expansions for a special function which appears in nonparametric estimation of log-densities. This function returns the integral of a log-linear function on a simplex of arbitrary dimension.…
In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration. Under the condition (A), we get an integral representation formula for the…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
We prove that any power of the logarithm of Fourier series with random signs is integrable. This result has applications to the distribution of values of random Taylor series, one of which answers a long-standing question by J.-P. Kahane.
This is a literal word-for-word translation from the French of Phragmen's proof (the first such published) of Weierstrass' famous theorem characterizing all analytic functions which possess an algebraic addition theorem.
Some notes and observations on analytic functions defined on an annulus
We prove a Log Log inequality with a sharp constant in four dimensions for radially symmetric functions. We also show that the constant in the Log estimate is almost sharp.
In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials.…
In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete…
We propose the Lie-algebraic interpretation of poly-analytic functions in $L_2(\C,d\mu)$, with the Gaussian measure $d\mu$, based on a flag structure formed by the representation spaces of the $\mathfrak{sl}(2)$-algebra realized by…
It is known that rational approximations of elementary analytic functions (exp, log, trigonometric, and hyperbolic functions, and their inverse functions) are computable in the weak complexity class $\mathrm{TC}^0$. We show how to formalize…
We show by a dynamical argument that there is a positive integer valued function $q$ defined on positive integer set $\mathbb N$ such that $q([\log n]+1)$ is a super-polynomial with respect to positive $n$ and \[\liminf_{n\rightarrow\infty}…
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular…
We show that differentiable functions, defined on a convex body $K \subseteq \mathbb R^d$, whose derivatives do not exceed a suitable given sequence of positive real numbers share many properties with polynomials. The role of the degree of…
In the present paper we extend the multiplicative integral to complex-valued functions of complex variable. The main difficulty in this way, that is the multi-valued nature of the complex logarithm, is avoided by division of the interval of…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
Two theorems on the asymptotic distribution of zeros of sequences of analytic functions are proved. First one relates the asymptotic behavior of zeros to the asymptotic behavior of coefficients. Second theorem establishes a relation between…