Related papers: Complex Iterations of Entire Functions

A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…

We apply some methods and technique of complex dynamics to study the set of symmetries of attractors of holomorphic Iterated Function Systems (IFS), as well as relations between IFS sharing the same attractor.

Let $f$ be an inner function with $f(0)=0$ which is not a rotation and let $f^{n}$ be its $n$-th iterate. Let $\{a_{n}\}$ be a sequence of complex numbers. We prove that the series $\sum a_{n}f^{n}(\xi)$ converges at almost every point…

In this paper, we study cut sets of attractors of iteration function systems (IFS) in $\mathbb{R}^d$. Under natural conditions, we show that all irreducible cut sets of these attractors are perfect sets or single points. This leads to a…

Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…

We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…

In this article, the dynamics of a one-parameter family of functions $f_{\lambda}(z) = \frac{\sin{z}}{z^2 + \lambda},$ $\lambda>0$, are studied. It shows the existence of parameters $0< \lambda_{1}< \lambda_{2}$ such that bifurcations occur…

Let $\Phi$ be a continuous $n\times n$ matrix-valued function on the unit circle $\T$ such that the $(k-1)$th singular value of the Hankel operator with symbol $\Phi$ is greater than the $k$th singular value. In this case, it is well-known…

We study algorithms for the fast computation of modular inverses. Newton-Raphson iteration over $p$-adic numbers gives a recurrence relation computing modular inverse modulo $p^m$, that is logarithmic in $m$. We solve the recurrence to…

We provide a partial answer to the following problem: \emph{give an effective upper bound on the multiplicity of non-isolated common zero of a tuple of Noetherian functions}. More precisely, consider a foliation defined by two commuting…

In this presentation we shall deal with some aspects of the theory of Hilbert functions of modules over local rings, and we intend to guide the reader along one of the possible routes through the last three decades of progress in this area…

Newton iteration (NI) is an almost 350 years old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. In this…

In this paper we give the complete characterization of the boundedness of the generalized fractional maximal operator $$ M_{\phi,\Lambda^{\alpha}(b)}f(x) : = \sup_{Q \ni x} \frac{\|f \chi_Q\|_{\Lambda^{\alpha}(b)}}{\phi (|Q|)} \qquad (x \in…

multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…

We continue the study of the bosonic $O(N)^3$ model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant $\phi^4$ composite operators, known as tetrahedron, pillow and double-trace. As…

For a rational matrix function $\Phi$ with poles outside the unit circle, we estimate the degree of the unique superoptimal approximation $\A\Phi$ by matrix functions analytic in the unit disk. We obtain sharp estimates in the case of…

This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions of unitary operators. Starting from a given unitary…

Let $\phi:M_n\to B(H)$ be an injective, completely positive contraction with $\V\phi^{-1}:\phi(M_n)\to M_n\V_{cb}\leq1+\delta(\epsilon).$ We show that if either (i) $\phi(M_n)$ is faithful modulo the compact operators or (ii) $\phi(M_n)$…

Given a family $X$ of complex varieties degenerating over a punctured disc, one is interested in computing related invariants called the motivic nearby fiber and the refined limit mixed Hodge numbers, both of which contain information about…

This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…