The Logarithmic Integral, Volume 1The theme of this unique work, the logarithmic integral, lies athwart much of twentieth century analysis. It is a thread connecting many apparently separate parts of the subject, and so is a natural point at which to begin a serious study of real and complex analysis. Professor Koosis' aim is to show how, from simple ideas, one can build up an investigation which explains and clarifies many different, seemingly unrelated problems; to show, in effect, how mathematics grows. The presentation is straightforward, so this, the first of two volumes, is self-contained, but more importantly, by following the theme, Professor Koosis has produced a work that can be read as a whole. He has brought together here many results, some unpublished, some new, and some available only in inaccessible journals. |
Contents
III | 1 |
IV | 7 |
V | 10 |
VI | 13 |
VII | 15 |
VIII | 19 |
IX | 23 |
X | 37 |
LXXV | 280 |
LXXVI | 292 |
LXXVII | 305 |
LXXVIII | 306 |
LXXIX | 312 |
LXXX | 316 |
LXXXI | 318 |
LXXXII | 319 |
XI | 39 |
XIII | 43 |
XIV | 47 |
XV | 52 |
XVI | 58 |
XVII | 59 |
XVIII | 65 |
XIX | 69 |
XX | 78 |
XXI | 80 |
XXII | 83 |
XXIV | 89 |
XXVI | 92 |
XXVII | 97 |
XXVIII | 102 |
XXIX | 103 |
XXX | 109 |
XXXI | 110 |
XXXII | 116 |
XXXIII | 126 |
XXXV | 131 |
XXXVI | 132 |
XXXVIII | 142 |
XXXIX | 145 |
XL | 147 |
XLIII | 150 |
XLIV | 158 |
XLVI | 160 |
XLVII | 163 |
XLVIII | 165 |
XLIX | 169 |
L | 171 |
LIII | 175 |
LIV | 180 |
LV | 184 |
LVI | 187 |
LVII | 190 |
LVIII | 198 |
LIX | 203 |
LX | 209 |
LXII | 211 |
LXIII | 212 |
LXIV | 219 |
LXV | 233 |
LXVI | 234 |
LXVII | 235 |
LXVIII | 236 |
LXIX | 239 |
LXX | 243 |
LXXI | 250 |
LXXII | 251 |
LXXIII | 265 |
LXXIV | 275 |
LXXXIII | 323 |
LXXXIV | 327 |
LXXXV | 336 |
LXXXVI | 338 |
LXXXVII | 343 |
LXXXVIII | 348 |
LXXXIX | 356 |
XC | 374 |
XCI | 384 |
XCII | 386 |
XCIII | 387 |
XCIV | 400 |
XCVI | 404 |
XCVII | 411 |
XCVIII | 413 |
XCIX | 424 |
C | 432 |
CI | 434 |
CII | 443 |
CIII | 445 |
CIV | 446 |
CV | 447 |
CVI | 454 |
CVII | 468 |
CVIII | 473 |
CIX | 478 |
CXI | 484 |
CXII | 487 |
CXIII | 492 |
CXIV | 495 |
CXV | 497 |
CXVI | 506 |
CXVII | 516 |
CXVIII | 518 |
CXIX | 522 |
CXX | 525 |
CXXI | 526 |
CXXIII | 540 |
CXXV | 545 |
CXXVI | 548 |
CXXVII | 553 |
CXXVIII | 555 |
CXXX | 561 |
CXXXI | 568 |
CXXXII | 570 |
CXXXV | 574 |
CXXXVI | 582 |
CXXXVII | 590 |
CXXXVIII | 596 |
600 | |
CXL | 603 |
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Common terms and phrases
absolutely convergent Akhiezer's analytic approximation argument assume B₁ bounded Chapter concave conformal mapping const constant continuous convex corollary Cw(R denote domain du(t du(x dx dy entire function equal estimate exponential type Figure finite sums fixed formula function f(z given Green's Green's function half plane harmonic function harmonic measure hence hypothesis increasing inequality integral intervals Jensen's formula lemma limsup Lindelöf's theorem linear log T(r log W(x log+ log|f(z log|P(x logarithmic modulus obtain Phragmén-Lindelöf Phragmén-Lindelöf theorem polynomials positive measure preceding article previous article previous relation problem Proof proved real axis Remark result Riesz Scholium second theorem sequence slope subharmonic Suppose supremum theorem of article unit circumference unit disk vanishes Volberg's w-dense wlog write x2 dx