Topic

# Space (mathematics)

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

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01 Jan 1996

Abstract: ‘The Production of Space’, in: Frans Jacobi, Imagine, Space Poetry, Copenhagen, 1996, unpaginated.

6,698 citations

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01 Nov 1971

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.

5,406 citations

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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.

4,161 citations

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01 Jan 1983

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.

3,868 citations

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Abstract: The book is a search for a reconciliation between mental space (the space of the philosophers) and real space (the physical and social spheres in which we all live). In the course of his exploration, Henri Lefebvre moves from metaphysical and ideological considerations of the meaning of space to its experience in the everyday life of home and city. He seeks, in other words, to bridge the gap between the realms of theory and practice, between the mental and the social, and between philosophy and reality. In doing so, he ranges through art, literature, architecture and economics, and further provides a powerful antidote to the sterile and obfuscatory methods and theories characteristic of much recent continental philosophy.

2,413 citations