000			03530nam a22004693i 4500
001			EBC5295324
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005			20240729131757.0
006			m o d |
007			cr cnu||||||||
008			240724s2014 xx o ||||0 eng d
020			_a9781470418946 _q(electronic bk.)
020			_z9781470416669
035			_a(MiAaPQ)EBC5295324
035			_a(Au-PeEL)EBL5295324
035			_a(OCoLC)890464618
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA691 .T68 2014
082	0		_a516/.158
100	1		_aTotik, Vilmos.
245	1	0	_aPolynomial Approximation on Polytopes.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2014.
264		4	_c©2014.
300			_a1 online resource (124 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.232
505	0		_aCover -- Title page -- Part \ 1 . The continuous case -- Chapter 1. The result -- Chapter 2. Outline of the proof -- Chapter 3. Fast decreasing polynomials -- Chapter 4. Approximation on simple polytopes -- Chapter 5. Polynomial approximants on rhombi -- Chapter 6. Pyramids and local moduli on them -- Chapter 7. Local approximation on the sets ₐ -- Chapter 8. Global approximation of = _{ } on _{1/32} excluding a neighborhood of the apex -- Chapter 9. Global approximation of on _{1/64} -- Chapter 10. Completion of the proof of Theorem 1.1 -- Chapter 11. Approximation in \R^{ } -- Chapter 12. A -functional and the equivalence theorem -- Part \ 2 . The ^{ }-case -- Chapter 13. The ^{ } result -- Chapter 14. Proof of the ^{ } result -- Chapter 15. The dyadic decomposition -- Chapter 16. Some properties of ^{ } moduli of smoothness -- Chapter 17. Local ^{ } moduli of smoothness -- Chapter 18. Local approximation -- Chapter 19. Global ^{ } approximation excluding a neighborhood of the apex -- Chapter 20. Strong direct and converse inequalities -- Chapter 21. The -functional in ^{ } and the equivalence theorem -- Acknowledgement -- Bibliography -- Back Cover.
520			_aPolynomial approximation on convex polytopes in \mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aGeometry, Riemannian.
650		0	_aOrthogonal polynomials.
650		0	_aPolytopes.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aTotik, Vilmos _tPolynomial Approximation on Polytopes _dProvidence : American Mathematical Society,c2014 _z9781470416669
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5295324 _zClick to View
999			_c136280 _d136280