A Course in Approximation Theory

Thistextbookisdesignedforgraduatestudentsinmathematics,physics,engineering,andcomputerscience.Itspurposeistoguidethereaderinexploringcontemporaryapproximationtheory.Theemphasisisonmulti-variableapproximationtheory,i.e.,theapproximationoffunctionsinseveralvariables,asopposedtotheclassicaltheoryoffunctionsinonevariable.Mostofthetopicsinthebook,heretoforeaccessibleonlythroughresearchpapers,aretreatedherefromthebasicstothecurrentlyactiveresearch,oftenmotivatedbypracticalproblemsarisingindiverseapplicationssuchasscience,engineering,geophysics,andbusinessandeconomics.Amongthesetopicsareprojections,interpolationparadigms,positivedefinitefunctions,interpolationtheoremsofSchoenbergandMicchelli,tomography,artificialneuralnetworks,wavelets,thin-platesplines,boxsplines,ridgefunctions,andconvolutions.Animportantandvaluablefeatureofthebookisthebibliographyofalmost600itemsdirectingthereadertoimportantbooksandresearchpapers.Thereare438problemsandexercisesscatteredthroughthebookallowingthestudentreadertogetabetterunderstandingofthesubject.