{totalEditions, plural,
 =0 {# editions }
 one {# edition }
 other {# editions }
 }
 {totalHoldingCount, plural,
 =0 {in # libraries}
 one {in # library}
 other {in # libraries}
 }

This edition in {totalHoldingCount} libraries

{libraryName} added to favorite libraries

{libraryName} removed from favorite libraries

Better World Books

Bookshop.org

RightFind

AbeBooks

VitalSource

Amazon

Select this title to view the detailed record for {title}

Added: {formattedDate}

New at the library

Fiction

Showing {0}-{1} of {total} items

Nonfiction

View access options

Access from your libraries

Borrow from {library}

{formattedDistance} away

Borrow

Borrow from {institution} near {location}

Access Online

Request this item via:

Get it from {institution}

Borrow from your library

Borrow from {institution}

Unable to find any access options. Search the library catalog.

Cite list {title}

Cite

Cite {itemTitle}

Share {itemTitle}

Check out this item I found on https://search.worldcat.org

Add {itemTitle} to a list

Share

Add to list

Share list {title}

Item shared from WorldCat.org

Edition

Publisher

View all Formats and Editions for {title}

Dissertation

View all formats and editions

Unable to find libraries on WorldCat with this item.

Access

Yes, show me

Generating recommendations...

We have made recommendations based on your search.

Recommendations provided by a third-party AI service. Only title and author data is shared.

Looks like we hit a snag. Please try again later.

Let us know how we did

beta

We can make recommendations based on this item.

Recommendations for you

Explore similar titles

Uh oh! :(

Sign in

Please sign in to generate recommendations.

ISSN

Cast

Language Notes

Notes

Genre

ISBN

Subjects

Medium of Performance

Event Notes

Reproduction Notes

Show less information

Series

Publication

Credits

Show more information

Performers

Additional Physical Form Entry

Click this link to view the DOI record {x}

Physical Description

OCLC Number / Unique Identifier

Target Audience

Numeric Designation of Musical Work

More Information

Cartographic Mathematical Data

We tailor your experience based on the order of your favorite libraries.

Drag or select a library from below to update the order

use the arrow up and down keys to change the order

{0}, order {1} in the list of {2} libraries

Unable to save libraries order. Please try again

To save changes to the library order, press Done

WorldCat.org

PrefacePrologue: The Exponential FunctionChapter 1: Abstract IntegrationSet-theoretic notations and terminologyThe concept of measurabilitySimple functionsElementary properties of measuresArithmetic in [0, ∞]Integration of positive functionsIntegration of complex functionsThe role played by sets of measure zeroExercisesChapter 2: Positive Borel MeasuresVector spacesTopological preliminariesThe Riesz representation theoremRegularity properties of Borel measuresLebesgue measureContinuity properties of measurable functionsExercisesChapter 3: Lp-SpacesConvex functions and inequalitiesThe Lp-spacesApproximation by continuous functionsExercisesChapter 4: Elementary Hilbert Space TheoryInner products and linear functionalsOrthonormal setsTrigonometric seriesExercisesChapter 5: Examples of Banach Space TechniquesBanach spacesConsequences of Baire's theoremFourier series of continuous functionsFourier coefficients of L1-functionsThe Hahn-Banach theoremAn abstract approach to the Poisson integralExercisesChapter 6: Complex MeasuresTotal variationAbsolute continuityConsequences of the Radon-Nikodym theoremBounded linear functionals on LpThe Riesz representation theoremExercisesChapter 7: DifferentiationDerivatives of measuresThe fundamental theorem of CalculusDifferentiable transformationsExercisesChapter 8: Integration on Product SpacesMeasurability on cartesian productsProduct measuresThe Fubini theoremCompletion of product measuresConvolutionsDistribution functionsExercisesChapter 9: Fourier TransformsFormal propertiesThe inversion theoremThe Plancherel theoremThe Banach algebra L1ExercisesChapter 10: Elementary Properties of Holomorphic FunctionsComplex differentiationIntegration over pathsThe local Cauchy theoremThe power series representationThe open mapping theoremThe global Cauchy theoremThe calculus of residuesExercisesChapter 11: Harmonic FunctionsThe Cauchy-Riemann equationsThe Poisson integralThe mean value propertyBoundary behavior of Poisson integralsRepresentation theoremsExercisesChapter 12: The Maximum Modulus PrincipleIntroductionThe Schwarz lemmaThe Phragmen-Lindelöf methodAn interpolation theoremA converse of the maximum modulus theoremExercisesChapter 13: Approximation by Rational FunctionsPreparationRunge's theoremThe Mittag-Leffler theoremSimply connected regionsExercisesChapter 14: Conformal MappingPreservation of anglesLinear fractional transformationsNormal familiesThe Riemann mapping theoremThe class LContinuity at the boundaryConformal mapping of an annulusExercisesChapter 15: Zeros of Holomorphic FunctionsInfinite ProductsThe Weierstrass factorization theoremAn interpolation problemJensen's formulaBlaschke productsThe Müntz-Szas theoremExercisesChapter 16: Analytic ContinuationRegular points and singular pointsContinuation along curvesThe monodromy theoremConstruction of a modular functionThe Picard theoremExercisesChapter 17: Hp-SpacesSubharmonic functionsThe spaces Hp and NThe theorem of F. and M. RieszFactorization theoremsThe shift operatorConjugate functionsExercisesChapter 18: Elementary Theory of Banach AlgebrasIntroductionThe invertible elementsIdeals and homomorphismsApplicationsExercisesChapter 19: Holomorphic Fourier TransformsIntroductionTwo theorems of Paley and WienerQuasi-analytic classesThe Denjoy-Carleman theoremExercisesChapter 20: Uniform Approximation by PolynomialsIntroductionSome lemmasMergelyan's theoremExercisesAppendix: Hausdorff's Maximality TheoremNotes and CommentsBibliographyList of Special SymbolsIndex

This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level--Publisher's description

Real and complex analysis