scispace - formally typeset
Search or ask a question
Topic

Space (mathematics)

About: Space (mathematics) is a research topic. Over the lifetime, 43093 publications have been published within this topic receiving 572779 citations. The topic is also known as: mathematical space.


Papers
More filters
Book Chapter
01 Jan 1996
TL;DR: In this article, Jacobi describes the production of space poetry in the form of a poetry collection, called Imagine, Space Poetry, Copenhagen, 1996, unpaginated and unedited.
Abstract: ‘The Production of Space’, in: Frans Jacobi, Imagine, Space Poetry, Copenhagen, 1996, unpaginated.

7,238 citations

Book
01 Nov 1971
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.
Abstract: The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

5,579 citations

Journal ArticleDOI
TL;DR: The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set and is separable and has optimal decay properties in both real and Fourier space.
Abstract: We present pseudopotential coefficients for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, seven coefficients are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive atomic and molecular test calculations. \textcopyright{} 1996 The American Physical Society.

5,009 citations

Book
01 Jan 1983
TL;DR: In this article, the authors measure smoothness using Atoms and Pointwise Multipliers, Wavelets, Spaces on Lipschitz Domains, Wavelet and Sampling Numbers.
Abstract: How to Measure Smoothness.- Atoms and Pointwise Multipliers.- Wavelets.- Spaces on Lipschitz Domains, Wavelets and Sampling Numbers.- Anisotropic Function Spaces.- Weighted Function Spaces.- Fractal Analysis: Measures, Characteristics, Operators.- Function Spaces on Quasi-metric Spaces.- Function Spaces on Sets.

4,099 citations


Network Information
Related Topics (5)
Quantum field theory
24.6K papers, 749.9K citations
85% related
Invariant (mathematics)
48.4K papers, 861.9K citations
85% related
Eigenvalues and eigenvectors
51.7K papers, 1.1M citations
84% related
Differential equation
88K papers, 2M citations
84% related
Hamiltonian (quantum mechanics)
48.6K papers, 1M citations
83% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202264
20212,398
20202,199
20192,134
20182,102
20171,810