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001			EBC3114219
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006			m o d |
007			cr cnu||||||||
008			240724s2008 xx o ||||0 eng d
020			_a9781470405038 _q(electronic bk.)
020			_z9780821840634
035			_a(MiAaPQ)EBC3114219
035			_a(Au-PeEL)EBL3114219
035			_a(CaPaEBR)ebr11039838
035			_a(OCoLC)922981751
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA353.E5 -- G367 2008eb
082	0		_a510 s;515/.98
100	1		_aGanzburg, Michael I.
245	1	0	_aLimit Theorems of Polynomial Approximation with Exponential Weights.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2008.
264		4	_c©2008.
300			_a1 online resource (178 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.192
505	0		_aIntro -- Contents -- Chapter 1. Introduction -- 1.1. A Brief Review -- 1.2. Results and Organization of the Monograph -- 1.3. Basic Notation and Some Preliminaries -- 1.4. Classes of Weights and Basic Estimates -- 1.5. Acknowledgements -- Chapter 2. Statement of Main Results -- 2.1. Limit Theorems of Polynomial Approximation with Exponential Weights -- 2.2. Approximation of Entire Functions of Exponential Type -- 2.3. Polynomial Inequalities in the Complex Plane -- Chapter 3. Properties of Harmonic Functions -- 3.1. The Poisson Integral Re H(w) -- 3.2. The Function h(r) and the Constant b[sub(n)] -- 3.3. The Functions φ(r) and φ[sub(1)](r) -- 3.4. The Main Estimate for Re H(w) -- Chapter 4. Polynomial Inequalities with Exponential Weights -- 4.1. Nikolskii-type Inequalities -- 4.2. Extremal Polynomials -- 4.3. Polynomial Inequalities in the Complex Plane -- 4.4. Proofs of Theorems 2.3.1 and 2.3.2 -- Chapter 5. Entire Functions of Exponential Type and their Approximation Properties -- 5.1. Entire Functions of Exponential Type -- 5.2. Approximation Properties of Entire Functions of Exponential Type -- Chapter 6. Polynomial Interpolation and Approximation of Entire Functions of Exponential Type -- 6.1. Interpolation on the Interval I[sub(n)] = [ a[sub(n)](1+δ[sub(n)]), a[sub(n)](1+δ[sub(n)])] -- 6.2. Interpolation on I\I[sub(n)] -- 6.3. Proof of Theorem 2.2.1 -- 6.4. Proof of Theorem 2.2.2 -- Chapter 7. Proofs of the Limit Theorems -- 7.1. Proof of Theorem 2.1.1 -- 7.2. Proof of Theorem 2.1.2 -- 7.3. Proofs of Theorems 2.1.3 and 2.1.4 -- Chapter 8. Applications -- 8.1. Approximation of Individual Functions and Proof of Theorem 2.3.3 -- 8.2. An Asymptotically Sharp Constant of Weighted Approximation on the Class W[sup(r)]H[sup(λ)][I] -- 8.3. Convergence of Polynomials and a Mehler-Heine Formula for Orthonormal Polynomials.
505	8		_aChapter 9. Multidimensional Limit Theorems of Polynomial Approximation with Exponential Weights -- 9.1. Multidimensional Limit Theorems with Exponential Weights -- 9.2. Proof of Theorem 9.1.3 -- 9.3. Proofs of Theorems 9.1.1 and 9.1.4 -- 9.4. Approximation of λ-Homogeneous Functions -- Chapter 10. Examples -- 10.1. W(x) = exp( |x|α), α &gt -- 1 -- 10.2. W(x) = exp(-|x|) -- 10.3. W(x) = exp( |x|α), 0&lt -- α &lt -- 1 -- 10.4. W(x) = exp( |x|α), α → ∞ -- 10.5. Examples of Erdös Weights -- Appendix A. Appendix. Negativity of a Kernel -- A. l. Statement of the Main Result -- A. 2. Some Technical Results -- A. 3. Proof of Proposition A.1.1 -- Bibliography -- Index.
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	_aFunctions, Entire.
650		0	_aApproximation theory.
650		0	_aPotential theory (Mathematics).
650		0	_aFourier analysis.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aGanzburg, Michael I. _tLimit Theorems of Polynomial Approximation with Exponential Weights _dProvidence : American Mathematical Society,c2008 _z9780821840634
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114219 _zClick to View
999			_c69750 _d69750