## Singular Integral EquationsThis work focuses on the distributional solutions of singular integral equations, progressing from basic concepts of the classical theory to the more difficult two-dimensional problems. |

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### Contents

II | 1 |

III | 2 |

IV | 3 |

V | 7 |

VI | 11 |

VII | 12 |

VIII | 13 |

IX | 15 |

LVI | 205 |

LVII | 209 |

LVIII | 217 |

LIX | 221 |

LX | 226 |

LXI | 231 |

LXII | 242 |

LXIV | 251 |

X | 18 |

XI | 26 |

XII | 30 |

XIII | 33 |

XIV | 35 |

XV | 38 |

XVI | 41 |

XVII | 43 |

XVIII | 46 |

XIX | 48 |

XX | 51 |

XXI | 52 |

XXII | 57 |

XXIII | 60 |

XXIV | 64 |

XXVI | 71 |

XXVII | 72 |

XXVIII | 75 |

XXIX | 78 |

XXX | 82 |

XXXI | 84 |

XXXII | 91 |

XXXIII | 93 |

XXXIV | 100 |

XXXV | 103 |

XXXVI | 108 |

XXXVII | 113 |

XXXVIII | 116 |

XL | 125 |

XLI | 127 |

XLII | 134 |

XLIII | 140 |

XLIV | 145 |

XLV | 150 |

XLVI | 152 |

XLVII | 161 |

XLVIII | 168 |

L | 175 |

LI | 176 |

LII | 180 |

LIII | 187 |

LIV | 191 |

LV | 196 |

LXV | 252 |

LXVI | 254 |

LXVII | 262 |

LXVIII | 264 |

LXIX | 270 |

LXX | 282 |

LXXI | 286 |

LXXII | 287 |

LXXIII | 295 |

LXXIV | 296 |

LXXV | 298 |

LXXVI | 300 |

LXXVII | 302 |

LXXVIII | 308 |

LXXIX | 311 |

LXXX | 313 |

LXXXI | 314 |

LXXXII | 318 |

LXXXIII | 322 |

LXXXIV | 323 |

LXXXV | 339 |

LXXXVI | 340 |

LXXXVII | 345 |

LXXXVIII | 355 |

LXXXIX | 361 |

XC | 369 |

XCII | 375 |

XCIII | 377 |

XCIV | 379 |

XCV | 382 |

XCVI | 384 |

XCVII | 386 |

XCVIII | 390 |

XCIX | 391 |

C | 395 |

CI | 399 |

CII | 401 |

CIII | 402 |

CIV | 403 |

413 | |

423 | |

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### Common terms and phrases

3m co analysis analytic representation arbitrary constant belongs Cauchy principal value Cauchy type integral chapter closed contour compute Consider the integral converges convolution decomposition denote differential distributional boundary values distributional solution dual integral equations dual space eigenvalues endpoints equa Erdelyi-Kober operators Example exists finite Fourier transform fractional integration func given half-plane Hankel transform Hilbert transform HINr improper integral infinity interval inverse isomorphism Laplace transform Lebesgue integral Lemma Let us consider locally integrable logarithmic kernels multiply never vanishes non-normal Observe obtain the solution open contour pole polynomial principal value relation Riemann-Hilbert problem satisfies sectionally analytic function Show singular integral equations smooth functions solution of equation solve the equation Solve the following Solve the integral spaces of distributions subspace summable Suppose test functions Theorem tion type integral equations upper half-plane Wiener-Hopf write zero

### Popular passages

Page 418 - The Hankel transform of some classes of generalized functions and connections with fractional integration. Proc. Roy. Soc.

Page 417 - H. Kober, On fractional integrals and derivatives, Quart. J. Math. Oxford Ser. 11 (1940), 193-211.

Page 417 - Kaya, AC and Erdogan, F. , On the Solution of Integral Equations with Strongly Singular Integrals, Q.

Page 420 - Boundary Value Problems of Mathematical Physics, Volume II, MacMillan, New York (1968).

Page 420 - Teixeira, FS, Theory of a class of WienerHopf equations of the first kind: application to the Sommerfeld problem,/ Math.