Hausdorff Approximations'Et moi, ... , si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point a1Ie.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. |
Contents
V | 1 |
VII | 2 |
IX | 4 |
XI | 5 |
XII | 7 |
XIII | 8 |
XV | 10 |
XVI | 12 |
LV | 128 |
LVI | 140 |
LVII | 142 |
LVIII | 157 |
LIX | 165 |
LX | 167 |
LXI | 174 |
LXII | 175 |
XVII | 13 |
XVIII | 15 |
XIX | 17 |
XX | 18 |
XXI | 23 |
XXII | 25 |
XXIII | 31 |
XXIV | 35 |
XXV | 40 |
XXVI | 42 |
XXVII | 44 |
XXVIII | 46 |
XXIX | 49 |
XXX | 54 |
XXXI | 55 |
XXXII | 57 |
XXXIII | 61 |
XXXIV | 64 |
XXXV | 67 |
XXXVI | 70 |
XXXVIII | 71 |
XL | 72 |
XLI | 78 |
XLII | 81 |
XLIII | 82 |
XLIV | 83 |
XLV | 84 |
XLVI | 85 |
XLVII | 96 |
XLVIII | 99 |
XLIX | 108 |
L | 109 |
LI | 112 |
LII | 120 |
LIV | 125 |
LXIII | 190 |
LXIV | 198 |
LXV | 203 |
LXVI | 206 |
LXVII | 212 |
LXVIII | 213 |
LXIX | 227 |
LXX | 233 |
LXXI | 234 |
LXXII | 244 |
LXXIII | 247 |
LXXIV | 255 |
LXXV | 257 |
LXXVI | 263 |
LXXVII | 264 |
LXXVIII | 270 |
LXXIX | 280 |
LXXX | 289 |
LXXXI | 291 |
LXXXII | 293 |
LXXXIV | 304 |
LXXXV | 308 |
LXXXVI | 315 |
LXXXVII | 318 |
LXXXVIII | 319 |
LXXXIX | 322 |
XCII | 323 |
XCIII | 326 |
XCIV | 327 |
| 333 | |
| 355 | |
| 361 | |
| 363 | |
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Common terms and phrases
absolute constant According algebraic polynomials arbitrary belongs best approximation best Hausdorff approximation bounded function Boyanov closed interval Cm,r completed graph completes the proof continuous functions convergence convex Corollary corridor corridor K definition denote Dk(f Dolzenko E(Hn E(Rn E(Tn elementary squares estimate exists finite function f H-continuity H-distance Hausdorff distance Hence holds If(x kp,q labyrinth last inequality Lemma lemma is proved Let fe lim sup linear operators Ln(f log2 lp,q modulus of continuity monotone functions obtain one-sided Hausdorff order no higher order of approximation polynomial of best polynomial oscillator Popov positive integer positive linear operators proof of Theorem rational function rectangle respect to Hausdorff satisfies segment functions Sendov Sevastianov Sk,n Slim spline functions subsets theorem is proved trigonometric polynomial uniform approximation uniform convergence uniform distance Veselinov zero αε ΧΕΔ