LEADER 03705nam 2200613 450 001 9910480612003321 005 20180613001258.0 010 $a1-4704-0114-2 035 $a(CKB)3360000000464719 035 $a(EBL)3113936 035 $a(SSID)ssj0000888821 035 $a(PQKBManifestationID)11453144 035 $a(PQKBTitleCode)TC0000888821 035 $a(PQKBWorkID)10865679 035 $a(PQKB)10803194 035 $a(MiAaPQ)EBC3113936 035 $a(PPN)195414187 035 $a(EXLCZ)993360000000464719 100 $a20140909h19941994 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aChristoffel functions and orthogonal polynomials for exponential weights on [?1, 1] /$fA. L. Levin, D. S. Lubinsky 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1994. 210 4$d©1994 215 $a1 online resource (166 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vNumber 535 300 $a"September 1994, Volume 111, Number 535 (fourth of 5 numbers)." 311 $a0-8218-2599-2 320 $aIncludes bibliographical references. 327 $a""Table of Contents""; ""A?1. Introduction and Results""; ""Definition 1.1: The class W""; ""Theorem 1.2: Christoffel Functions""; ""Corollary 1.3: Sup-Norms of Christoffel Functions""; ""Corollary 1.4: Zeros""; ""Corollary 1.5: Bounds on Orthonormal Polynomials""; ""Theorem 1.6: Sup-Norm Christoffel Functions""; ""Theorem 1.7: Restricted Range Inequalities""; ""Theorem 1.8: L[sub(p)] Norms of Orthonormal Polynomials""; ""A?2. Some Ideas Behind the Proofs""; ""I. An Orthogonal Polynomial Angle""; ""II. The Potential Theory Side: Lower Bounds for I?»[sub(n)]"" 327 $a""Proof of Theorem 4.2""""Proof of Theorem 4.3 (b)""; ""Proof of Theorem 4.3 (a)""; ""A?5. Majorization Functions and Integral Equations""; ""Lemma 5.1: Old Potential Theory/Integral Equations""; ""Lemma 5.2: Estimates for B[sub(n,R)],v[sub(n,R)]""; ""Theorem 5.3: Estimates for U[sub(n,R)]""; ""A?6. The Proof of Theorem 1.7""; ""Lemma 6.1: L[sub(p)] Bounds for Weighted Polynomials""; ""Proof of Theorem 1.7""; ""A?7. Lower Bounds for I?»[sub(n)]""; ""Theorem 7.1: Lower Bounds for I??[sub(n)]""; ""Lemma 7.2: Preliminary Lower Bounds""; ""Proof of Theorem 7.1"" 327 $a""A?8. Discretisation of a Potential: Theorem 1.6""""Theorem 8.1: One Point Polynomials""; ""Deduction of Theorem 1.6""; ""Theorem 8.2: The Bounds for I??[sub(n)]""; ""Deduction of Theorem 8.1""; ""Lemma 8.3: Estimates for the discretisation points""; ""Lemma 8.4: Estimates for S[sub(1)]+[sub(4)]""; ""Lemma 8.5: Estimates for I??[sub(j)]""; ""Lemma 8.6: Estimates for I??[sub(j)]""; ""Lemma 8.7: Estimates for S[sub(21)]""; ""Lemma 8.8: Lower Bounds for S[sub(2)]""; ""Lemma 8.9: Upper Bounds for S[sub(2)]""; ""Lemma 8.10: Bounds for S[sub(3)]""; ""Proof of Theorem 8.2"" 327 $a""Lemma 11.5: An Estimate for I[sub(3)]"" 410 0$aMemoirs of the American Mathematical Society ;$vNumber 535. 606 $aOrthogonal polynomials 606 $aChristoffel-Darboux formula 606 $aConvergence 608 $aElectronic books. 615 0$aOrthogonal polynomials. 615 0$aChristoffel-Darboux formula. 615 0$aConvergence. 676 $a515/.55 700 $aLevin$b A. L.$f1944-$0768216 702 $aLubinsky$b D. S$g(Doron Shaul),$f1955- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480612003321 996 $aChristoffel functions and orthogonal polynomials for exponential weights on$92218894 997 $aUNINA LEADER 05392nam 2200685Ia 450 001 9910784656903321 005 20220609133716.0 010 $a1-280-70770-4 010 $a9786610707706 010 $a0-08-046545-5 035 $a(CKB)1000000000364033 035 $a(EBL)281971 035 $a(OCoLC)437175524 035 $a(SSID)ssj0000109111 035 $a(PQKBManifestationID)11138073 035 $a(PQKBTitleCode)TC0000109111 035 $a(PQKBWorkID)10045428 035 $a(PQKB)10514350 035 $a(Au-PeEL)EBL281971 035 $a(CaPaEBR)ebr10151448 035 $a(CaONFJC)MIL70770 035 $a(CaSebORM)9780123735898 035 $a(MiAaPQ)EBC281971 035 $a(EXLCZ)991000000000364033 100 $a20060615d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBasics of interferometry /$fP. Hariharan 205 $a2nd ed. 210 $aBoston $cElsevier Academic Press$dc2006 215 $a1 online resource (249 p.) 300 $aDescription based upon print version of record. 311 0 $a9781493301003 (Paperback) 311 0 $a0-08-046545-5 (PDF) 311 0 $a1-280-70770-4 (Electronic Book) 311 0 $a0-12-373589-0 (Hardback) 320 $aIncludes bibliographical references and index. 327 $aFront cover; Title page; Copyright page; Contents; Preface to the First Edition; Preface to the Second Edition; Acknowledgments; 1 Introduction; 2 Interference: A Primer; 2.1 Light Waves; 2.2 Intensity in an Interference Pattern; 2.3 Visibility of Interference Fringes; 2.4 Interference with a Point Source; 2.5 Localization of Fringes; 2.6 Summary; 2.7 Problems; Further Reading; 3 Two-Beam Interferometers; 3.1 Wavefront Division; 3.2 Amplitude Division; 3.3 The Rayleigh Interferometer; 3.4 The Michelson Interferometer; 3.5 The Mach-Zehnder Interferometer; 3.6 The Sagnac Interferometer 327 $a3.7 Summary 3.8 Problems; Further Reading; 4 Source-Size and Spectral Effects; 4.1 Coherence; 4.2 Source-Size Effects; 4.3 Spectral Effects; 4.4 Polarization Effects; 4.5 White-Light Fringes; 4.6 Channeled Spectra; 4.7 Summary; 4.8 Problems; Further Reading; 5 Multiple-Beam Interference; 5.1 Multiple-Beam Fringes by Transmission; 5.2 Multiple-Beam Fringes by Reflection; 5.3 Multiple-Beam Fringes of Equal Thickness; 5.4 Fringes of Equal Chromatic Order (FECO Fringes); 5.5 The Fabry-Perot Interferometer; 5.6 Summary; 5.7 Problems; Further Reading; 6 The Laser as a Light Source 327 $a6.1 Lasers for Interferometry 6.2 Laser Modes; 6.3 Single-Wavelength Operation of Lasers; 6.4 Polarization of Laser Beams; 6.5 Wavelength Stabilization of Lasers; 6.6 Laser-Beam Expansion; 6.7 Problems with Laser Sources; 6.8 Laser Safety; 6.9 Summary; 6.10 Problems; Further Reading; 7 Photodetectors; 7.1 Photomultipliers; 7.2 Photodiodes; 7.3 Charge-Coupled Detector Arrays; 7.4 Photoconductive Detectors; 7.5 Pyroelectric Detectors; 7.6 Summary; 7.7 Problems; Further Reading; 8 Measurements of Length; 8.1 The Definition of the Metre; 8.2 Length Measurements 327 $a8.3 Measurements of Changes in Length 8.4 Summary; 8.5 Problems; Further Reading; 9 Optical Testing; 9.1 The Fizeau Interferometer; 9.2 The Twyman-Green Interferometer; 9.3 Analysis of Wavefront Aberrations; 9.4 Laser Unequal-Path Interferometers; 9.5 The Point-Diffraction Interferometer; 9.6 Shearing Interferometers; 9.7 Grazing-Incidence Interferometry; 9.8 Summary; 9.9 Problems; Further Reading; 10 Digital Techniques; 10.1 Digital Fringe Analysis; 10.2 Digital Phase Measurements; 10.3 Testing Aspheric Surfaces; 10.4 Summary; 10.5 Problems; Further Reading; 11 Macro- and Micro-Interferometry 327 $a11.1 Interferometry of Refractive Index Fields 11.2 The Mach-Zehnder Interferometer; 11.3 Interference Microscopy; 11.4 Multiple-Beam Interferometry; 11.5 Two-Beam Interference Microscopes; 11.6 The Nomarski Interferometer; 11.7 Summary; 11.8 Problems; Further Reading; 12 White-Light Interference Microscopy; 12.1 White-Light Interferometry; 12.2 White-Light Phase-Shifting Microscopy; 12.3 Spectrally Resolved Interferometry; 12.4 Coherence-Probe Microscopy; 12.5 Summary; 12.6 Problems; Further reading; 13 Holographic and Speckle Interferometry; 13.1 Holographic Interferometry 327 $a13.2 Holographic Nondestructive Testing 330 $aOptical interferometry is used in communications, medical imaging, astronomy, and structural measurement. With the use of an interferometer engineers and scientists are able to complete surface inspections of micromachined surfaces and semiconductors. Medical technicians are able to give more concise diagnoses with the employ of interferometers in microscopy, spectroscopy, and coherent tomography.Originating from a one-day course, this material was expanded to serve as an introduction to the topic for engineers and scientists that have little optical knowledge but a need for more in the 606 $aInterferometry 606 $aElectric interference 615 0$aInterferometry. 615 0$aElectric interference. 676 $a535/.470287 700 $aHariharan$b P$047552 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784656903321 996 $aBasics of interferometry$92616738 997 $aUNINA