Wyniki wyszukiwania dla: RIEMANNIAN MANIFOLD · HESTENES OPERATOR · SMOOTH ORTHOGONAL PROJECTION · LATITUDINAL PROJECTION · SMOOTH DECOMPOSITION OF IDENTITY · MORSE FUNCTION · SOBOLEV SPACE

• Smooth Orthogonal Projections on Riemannian Manifold

  Publikacja

  • M. Bownik
  • K. Dziedziul
  • A. Kamont

  - POTENTIAL ANALYSIS - Rok 2021

  We construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, S´er. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const....

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• Harmonic Analysis

  Dane Badawcze

  open access

  • K. Dziedziul

  We construct a decomposition of the identity operator on a Riemannian manifold M as   a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, Sér. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser...

• Parseval Wavelet Frames on Riemannian Manifold

  Publikacja

  • M. Bownik
  • K. Dziedziul
  • A. Kamont

  - JOURNAL OF GEOMETRIC ANALYSIS - Rok 2021

  We construct Parseval wavelet frames in L 2 (M) for a general Riemannian manifold M and we show the existence of wavelet unconditional frames in L p (M) for 1 < p < ∞. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on L 2 (M), which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkin F sp,q (M) and Besov B...

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• Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere

  Publikacja

  • M. Bownik
  • K. Dziedziul
  • A. Kamont

  - JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS - Rok 2022

  We construct a single smooth orthogonal projection with desired localization whose average under a group action yields the decomposition of the identity operator. For any full rank lattice \Gamma ⊂ R^d , a smooth projection is localized in a neighborhood of an arbitrary precompact fundamental domain R^d / \Gamma. We also show the existence of a highly localized smooth orthogonal projection, whose Marcinkiewicz average under the...

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• Smooth orthogonal projections on sphere.

  Publikacja

  • M. Bownik
  • K. Dziedziul

  - CONSTRUCTIVE APPROXIMATION - Rok 2015

  We construct a decomposition of the identity operator on the sphere S^d as a sum of smooth orthogonal projections subordinate to an open cover of S^d. We give applications of our main result in the study of function spaces and Parseval frames on the sphere.

• The asymptotic formula for the error in orthogonal projection

  Publikacja

  • M. Beśka
  • K. Dziedziul

  - MATHEMATISCHE NACHRICHTEN - Rok 2002

  W pracy podano formułę asymptotyczną błędu aproksymacji dla rzutów ortogonalnych w normie L^p.

• Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers

  Publikacja

  • G. Graff
  • A. Kaczkowska

  - Annales Polonici Mathematici - Rok 2013

  Let f be a smooth self-map of an m-dimensional (m >3) closed connected and simply-connected manifold such that the sequence of the Lefschetz num- bers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defned in combinatorial terms and is...

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• Compressed Projection Bases for Model-Order Reduction of Multiport Microwave Components Using FEM

  Publikacja

  • M. Mul
  • D. Szypulski
  • G. Fotyga
  • M. Mrozowski

  - Rok 2019

  This paper presents a projection basis compression technique for generating compact reduced-order models (ROM) in the FE analysis of microwave devices. In this approach redundancy is removed from the projection basis by means of the proper orthogonal decomposition technique applied to the projected system of linear equations. Compression allows for keeping the size of a reduced-order model as small as possible without compromising...

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• Reasoning with Projection in Multimodular Description Logics Knowledge Bases

  Publikacja

  • K. Goczyła
  • A. Waloszek
  • W. Waloszek

  - Communications in Computer and Information Science - Rok 2014

  We present an approach to reasoning with projection, i.e. reasoning in which it is possible to focus on a selected part of knowledge (by neglecting some non-interesting fragments). Projection is most useful for modular knowledge bases in which only parts of knowledge have to be exchanged or imported to other modules. In this paper we present an optimized method of reasoning over results of projection. The tests indicate that the...

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• On the growth of the number of periodic points for smooth self maps of a compact manifold

  Publikacja

  • G. Graff
  • J. Jezierski

  - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY - Rok 2007

  Dla ciągłego przekształcenia jednospójnej rozmaitości wymiaru co najmniej 3 w siebie, wykazujemy, że wzrost liczby punktów r-periodycznych w klasie homotopii może być nie szybszy niż liniowy, dla dowolnego, ustalonego r.

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