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209

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Publications to appear (added after completion of the manuscript)

Dang Dinh Ang and R. Gorenflo: A nonlinear Abel integral equation. K.H. Hoffmannand W. Krabs(editors). Conference on Optimal Control Problems Governed by PartialDifferential Equations. Irsee, April 9-12, 1990.

Dang Dinh Ang, R. Gorenflo and Dang Dinh Hai: Regularization of a generalized Abelintegral equation. To appear in a journal.

R. Rutman and L. Estes: A systems theory model for inversion of the Abel transform.A. Vogel et alii( eds.): Proc. Seventh International Seminar on Model Optimization inExploration Geophysics. Berlin, February 6-10, 1989.

Subject Index 1

AAbel 1Abel's mechanical problem 26Adams 72Anderssen 57a priori bounds 103Arsenin 156Arzela-Ascoli theorem 79

BBanach 129Banach space 72Benndorf 50Bessanova 51Bessel function of first kind 113Borok 51Bosanquet 3Branca 185Brunner 7

CCalligaro 57Cameron 184Campi 51Cannon 139Carleman 63Cauchy principal value 122Chebyshev polynomials of first kind 118compact operator 6compactness of Abel operator 78convolution 64Cormack 4Cryer 191crystallography 39

DDahlquist 153Dirac's delta-function 43Dirichlet problem 141discrete probability 39

lwe mention"Abel" the first time that this name appears.

211

EEckhardtEdelsteinEdelstein's fixed point theoremEggermontelasticity theoryErdelyiErdelyi-Kober fractional operatorEuler beta functionEuler gamma functionevaluation of measurements

EFishmanflat earth modelFourier transformfractional derivative operatorfractional derivative of a composite functionfractional derivative of a product of functionsfractional integral operatorfractional integration by partsfractional power of an operatorFubini

GGarmanyGauss least squares fitGelfandgeneralized Abel equationsgeneralized functionsgeometric opticsGilbertGoldsmithGorenfloGram-matrixGroetshGronwall's inequality

76

132184

23

99112

185-191

5151-56

4398983

98318

51187

33

3951514918818715294

212

HHadamard 2Hairer 152Handelsman 150Hankel transform 4

3Hardy class 105Herglotz 50Hilbert-Riemann boundary value problem 63Hilbert transform 4Holder continuous spaces 69-72Holder's inequality 67Hormann 36Houwen 185hydrodynamics 61

Iill-posed problem 6integrated Lipschitz conditions 78interpolating quadrature methods 184inverse scattering problem for a repelling potential 31inversion of seismic travel times 50-56isochrone problem 12

L.Lame parameters 51Laplace transform 63Larkin 7Lebesgue 17Levinson 149Levy 188

152Liouville 3Littlewood 3

3Lowengrub 123

luminosity 38

213

MMackenzie 51Mann 129Marcuse 57Marcinkiewicz-Zygmund interpolation theorem 65

M1M

mechanics 2Meister 121Mellin transform 4metallography 39Minerbo 188Mittag-Leffler function 131moments 41Moran 39multiplicative convolution 108

NNagumo-type condition 132Natterer 190Neumann initial-boundary value problem 139Newton 142Newtonian cooling 142Newtonian heating 142Newton's law of cooling 139

oOlmstead 150optical fibres 56Orcutt 51oscillating pendulum 30Osler 3

I:Padmavally 148Paley-Wiener theorem 104paraxial ray equation 58Parker 51Parseval's relation 103partial differential equations 61Penzel 121Peters 121

214

photoelastic effectPicardplasma physicspressure wavesprobability densityprobability distribution

Qquadrat ure methods

RRadon transformrefractive index of optical fibresray parametersregularization by discretizationReinermannRieleRiemannRiemann-Liouville fractional operatorRiesz potentialsRobertsRunge-Kutta methodsRyaboyi

S.SakaljukSamkoscattering experimentsSchauder's fixed point theoremSchlichteSchwarz inequalityseismic travel timesseismic wavesseismologyshear wavesShibataShilovShmoysSitnikovaSnellius refraction lawSobolev spacessolution formulasspectroscopy

571292

503946

184-185

456-60

531906

1523995

1291.')251

6312121)

14815212550502

505733351515

222

215

stability estimatesstability results for the general linear Abel integral equationStallbohmstereologystereology of spherical particlesStieltjes integralStirling formulasuccessive approximation method

TTamarkintheory of elasticitytheory of scatteringTikhonovTikhonov regularizationtomato salad problemtomography of the earthTonellitrapezoidal product integration methodtravel time curveTricomi's equation

Vvan der HouwenVolterraVolterra integral equations

WWaltonweak singularitywell-posedWeylWeyI fractional operatorWiechertWiener-Hopf equationWolf

YYoungYoung's inequality

Zikoll

6168

62

39-492516783

322

1563848513

1845662

722

1732

49399504

139

365

7

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