Skip to main content
SpringerLink
Log in

Green’a Functions

  • Chapter
Integral Transforms and their Applications

Part of the book series: Applied Mathematical Sciences ((AMS,volume 25))

  • 533 Accesses

Abstract

One approach to the solution of non-homogeneous boundary value problems is by means of the construction of functions known as Green’s functions. Historically, the concept originated with work on potential theory published by Green in 1828. Green’s work has provided the germs of a much wider formulation for solving a variety of eigenvalue, boundary value, and inhomogeneous problems, particularly since the advent of generalized functions. We shall not attempt a systematic treatment in this book; rather we will discuss problems and methods where integral transform techniques are useful. In particular, we will discuss in this section problems where the Fourier transform in one variable is applicable.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Footnotes

  1. Excellent accounts are given in Stakgold (1968) and Morse ε Feshbach (1953), Ch. 7.

    Google Scholar 

  2. See Gelfand & Shilov (1964), pp. 39ff.

    Google Scholar 

  3. The difference between any two solutions of satisfies ∇2φ = 0; therefore we may write.

    Google Scholar 

  4. The normal derivative of (47) is a Fourier transform which is given in Problem 7.26.

    Google Scholar 

  5. This problem is adapted from a paper by W. E. Williams, Q. J. Mech. Appl. Math., (1973), 26, 397, where some more general results may be fo

    Article  MATH  Google Scholar 

  6. Problems 9–11 are based on results given by G. S. Argawal, A. J. Devaney and D. N. Pattenayak, J. Math. Phys. (1973), 14, 906.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The Australian National University, Post Office Box 4, Canberra, A.C.T., 2600, Australia

    B. Davies

Authors
  1. B. Davies
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer Science+Business Media New York

About this chapter

Cite this chapter

Davies, B. (1985). Green’a Functions. In: Integral Transforms and their Applications. Applied Mathematical Sciences, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-2691-3_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-2691-3_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96080-7

  • Online ISBN: 978-1-4899-2691-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation