Uniform approximation of functions in Jordan domains

The rate of polynomial approximation in the complex domain

Isomorphisms of the disc algebra and inverse faber sets

Recent work of Pavlov suggests the following definition: positive integers p 1 p 2 z p n } strongly nonspanning if the approximation, by linear combinations, to positive integral powers not in the sequence is uniformly bad for all curves extending from one circle about the origin to another; there is a related notion of strongly free sets. It is shown that for an interpolation sequence, the corresponding powers are strongly free and strongly nonspanning. As one corollary (implicit in Pavlov's work), an interpolation sequence { p n } is a Macintyre sequence: a non-constant entire function Σa n z p n can not be bounded on a curve going to infinity. Our interpolation sequences include the sequences of exponents which Kovari and Pavlov have identified as Macintyre sequences.

Interpolation, strongly nonspanning powers and Macintyre exponents

In order to describe quantum mechanical effects, the use of the von-Neumann equation is apparent. In this work, we present a unified numerical framework so that the von-Neumann equation in center-of-mass coordinates leads to a Quantum Liouville-type equation when choosing a suitable basis. In particular, the proposed approach can be related to the conventional Wigner equation when a plane wave basis is used. The drawback of the numerical methods is the high computational cost. Our presented approach is extended to allow reducing the dimension of the basis, which leads to a computationally efficient and accurate subdomain approach. Not only the steady-state behavior is of interest, but also the dynamic behavior. In order to solve the time-dependent case, suitable approximation methods for the time-dependent exponential integrator are necessary. For this purpose, we also investigate approximations of the exponential integrator based on Faber polynomials and Krylov methods. In order to evaluate and justify our approach, various test cases, including a resonant tunnel diode as well as a double-gate field-effect transistor, are investigated and validated for the stationary and the dynamic device behavior.

/pdf/subdomain-based-exponential-integrators-for-quantum-525lzxryyy.pdf

Subdomain-based exponential integrators for quantum Liouville-type equations

On the order of polynomial approximation for closed Jordan domains

On the asymptotic paths of entire functions with gap power series

The principal aim of this paper is to give an explicit construction for a sequence of polynomials that interpolates the function f on a given system of nodes and also converges to f uniformly. The functions we are able to approximate in this manner are continuous on the compact convex set K, and holomorphic in the interior of K.

On the uniform approximation of holomorphic functions on convex sets by means of interpolation polynomials

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Thomas Kövari

Author Tools

Chat about Author

Papers

On the order of polynomial approximation for closed Jordan domains

On the asymptotic paths of entire functions with gap power series

On the uniform approximation of holomorphic functions on convex sets by means of interpolation polynomials