Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Dirac delta function
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
==References== *{{citation |last1=Aratyn |first1=Henrik |last2=Rasinariu |first2 =Constantin| title=A short course in mathematical methods with Maple|url=https://books.google.com/books?id=JFmUQGd1I3IC&pg=PA314 |isbn=978-981-256-461-0 |publisher=World Scientific |year=2006}}. *{{Citation | last1=Arfken | first1=G. B. | author-link1=George B. Arfken | last2=Weber | first2=H. J. | title=Mathematical Methods for Physicists | publisher=[[Academic Press]] | location=Boston, Massachusetts | edition=5th | isbn=978-0-12-059825-0 | year=2000}}. * {{citation | author=atis | year = 2013 | title = ATIS Telecom Glossary | url = http://www.atis.org/glossary/definition.aspx?id=743| archive-url = https://web.archive.org/web/20130313211636/http://www.atis.org/glossary/definition.aspx?id=743 | archive-date = 2013-03-13 }} * {{citation | last=Bracewell |first= R. N.|author-link=Ronald N. Bracewell| title=The Fourier Transform and Its Applications| edition=2nd | publisher=McGraw-Hill | year=1986|bibcode= 1986ftia.book.....B}}. * {{citation | last=Bracewell |first= R. N.|author-link=Ronald N. Bracewell| title=The Fourier Transform and Its Applications| edition=3rd | publisher=McGraw-Hill | year=2000}}. * {{citation|title=La formule sommatoire de Poisson|first=A.|last=Córdoba|journal=Comptes Rendus de l'Académie des Sciences, Série I |year=1988 |volume=306|pages=373–376}}. * {{citation|first1=Richard|last1=Courant|author-link1=Richard Courant|first2=David|last2=Hilbert|author-link2=David Hilbert|title=Methods of Mathematical Physics, Volume II|publisher=Wiley-Interscience|year=1962}}. *{{citation|last1=Davis|first1=Howard Ted |last2=Thomson |first2=Kendall T |title=Linear algebra and linear operators in engineering with applications in Mathematica |url={{google books |plainurl=y |id=3OqoMFHLhG0C|page=344}} |year=2000|isbn=978-0-12-206349-7 |publisher=Academic Press}} *{{Citation | last1=Dieudonné | first1=Jean | author1-link=Jean Dieudonné | title=Treatise on analysis. Vol. II | publisher=Academic Press [Harcourt Brace Jovanovich Publishers] | location=New York | isbn=978-0-12-215502-4 | mr=0530406 | year=1976}}. *{{Citation | last1=Dieudonné | first1=Jean | author1-link=Jean Dieudonné | title=Treatise on analysis. Vol. III | publisher=Academic Press | location=Boston, Massachusetts | mr=0350769 | year=1972}} *{{citation|last=Dirac|first=Paul|author-link=Paul Dirac|year=1930|title=The Principles of Quantum Mechanics|edition=1st|publisher=Oxford University Press|title-link=The Principles of Quantum Mechanics}}. *{{citation|title=Encyclopedia of Optical Engineering|url=https://books.google.com/books?id=4hBTUY_2BMIC|first=Ronald G.|last=Driggers|year=2003|publisher=CRC Press|bibcode = 2003eoe..book.....D|isbn=978-0-8247-0940-2}}. *{{citation|last1=Duistermaat|first1=Hans|author-link1=Hans Duistermaat|last2=Kolk|title=Distributions: Theory and applications|publisher=Springer|year=2010}}. * {{citation | last = Federer | first = Herbert | author-link = Herbert Federer | title = Geometric measure theory|url=https://books.google.com/books?id=jld-BgAAQBAJ| publisher = Springer-Verlag | location = New York | year = 1969 | pages = xiv+676 | isbn = 978-3-540-60656-7 | mr= 0257325 | series = Die Grundlehren der mathematischen Wissenschaften| volume = 153 }}. * {{citation|last=Gannon|first=Terry|chapter=Vertex operator algebras|chapter-url=https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA539|title=Princeton Companion to Mathematics|publisher=Princeton University Press|year=2008|isbn=978-1400830398}}. *{{citation|first1=I. M.|last1=Gelfand|author-link1=Israel Gelfand|first2=G. E.|last2=Shilov|title=Generalized functions|url=https://books.google.com/books?id=nAnjBQAAQBAJ|volume=1–5|publisher=Academic Press|year=1966–1968|isbn=9781483262246}}. *{{citation |last=Hartmann |first=William M. |title=Signals, sound, and sensation |publisher=Springer |year=1997 |isbn=978-1-56396-283-7 |url=https://books.google.com/books?id=3N72rIoTHiEC}}. * <!-- Both 1995 and 2011 are required unless someone can confirm correct page numbers for the refs. Page 357 of 1995 does not match 357 in 2011 -->{{cite book |last1=Hazewinkel |first1=Michiel |title=Encyclopaedia of Mathematics (set) |date=1995 |publisher=Springer Science & Business Media |isbn=978-1-55608-010-4 |url=https://books.google.com/books?id=PE1a-EIG22kC&pg=PA357 |language=en}} * {{Cite book|first=Michiel|last=Hazewinkel|author-link=Michiel Hazewinkel|url={{google books |plainurl=y |id=_YPtCAAAQBAJ|}}|title=Encyclopaedia of mathematics|date=2011|publisher=Springer|isbn=978-90-481-4896-7|oclc=751862625|volume= 10}} *{{citation|last1=Hewitt|first1=E|author-link1=Edwin Hewitt|last2=Stromberg|first2=K|title=Real and abstract analysis|publisher=Springer-Verlag|year=1963}}. *{{citation|mr=0717035|first=L.|last= Hörmander|author-link=Lars Hörmander|title=The analysis of linear partial differential operators I|url=https://books.google.com/books?id=aaLrCAAAQBAJ|series= Grundl. Math. Wissenschaft. |volume= 256 |publisher= Springer |year=1983|isbn=978-3-540-12104-6 |doi=10.1007/978-3-642-96750-4}}. * {{citation|first=C. J.|last=Isham|title=Lectures on quantum theory: mathematical and structural foundations|url=https://books.google.com/books?id=dVs8PcZ0Hd8C|year=1995|publisher=Imperial College Press|bibcode=1995lqtm.book.....I |isbn= 978-81-7764-190-5}}. *{{Citation | last1=John | first1=Fritz |author-link=Fritz John| title=Plane waves and spherical means applied to partial differential equations |url=| publisher=Interscience Publishers, New York-London | mr=0075429 | year=1955 }}. [https://books.google.com/books?id=JP6ABuUnhecC Reprinted], Dover Publications, 2004, {{isbn|9780486438047}}. *{{Citation | last1=Lang | first1=Serge | author1-link=Serge Lang | title=Undergraduate analysis | publisher=Springer-Verlag | location=Berlin, New York | edition=2nd | series=[[Undergraduate Texts in Mathematics]] | isbn=978-0-387-94841-6 | mr=1476913 | year=1997 | doi=10.1007/978-1-4757-2698-5}}. *{{citation|last=Lange|first=Rutger-Jan|year=2012|title=Potential theory, path integrals and the Laplacian of the indicator|journal=Journal of High Energy Physics|volume=2012|pages=29–30|issue=11|bibcode=2012JHEP...11..032L|doi=10.1007/JHEP11(2012)032|arxiv = 1302.0864 |s2cid=56188533}}. *{{citation|doi=10.1007/BF00329867|author-link=Detlef Laugwitz|last=Laugwitz|first=D.|year=1989|title=Definite values of infinite sums: aspects of the foundations of infinitesimal analysis around 1820|journal=Arch. Hist. Exact Sci.|volume=39|issue=3|pages=195–245|s2cid=120890300}}. *{{Citation |title=An introduction to quantum theory |last=Levin |first=Frank S. |year=2002 |chapter-url=https://books.google.com/books?id=oc64f4EspFgC&pg=PA109 |pages=109''ff'' |chapter=Coordinate-space wave functions and completeness |isbn=978-0-521-59841-5 |publisher=Cambridge University Press}} *{{citation|last1=Li|first1=Y. T.|last2=Wong|first2=R.|mr=2373214|title=Integral and series representations of the Dirac delta function|journal=Commun. Pure Appl. Anal.|volume=7|year=2008|issue=2|doi=10.3934/cpaa.2008.7.229|pages=229–247|arxiv=1303.1943|s2cid=119319140}}. *{{cite thesis |last=de la Madrid Modino |first= R. |date=2001 |title= Quantum mechanics in rigged Hilbert space language|url=https://scholar.google.com/scholar?oi=bibs&cluster=2442809273695897641&btnI=1&hl=en |degree= PhD |publisher= Universidad de Valladolid}} *{{citation|doi=10.1002/1521-3978(200203)50:2<185::AID-PROP185>3.0.CO;2-S|first1=R.|last1=de la Madrid|first2=A.|last2=Bohm|first3=M.|last3=Gadella|title=Rigged Hilbert Space Treatment of Continuous Spectrum|arxiv=quant-ph/0109154|journal=Fortschr. Phys.|volume=50|year=2002|pages=185–216|issue=2|bibcode = 2002ForPh..50..185D |s2cid=9407651 }}. *{{citation|last=McMahon|first=D.|title=Quantum Mechanics Demystified, A Self-Teaching Guide|chapter-url=http://index-of.co.uk/Misc/McGraw-Hill%20-%20Quantum%20Mechanics%20Demystified%20(2006).pdf|access-date=2008-03-17|series=Demystified Series|date=2005-11-22|publisher=McGraw-Hill|location=New York|isbn=978-0-07-145546-6|page=108|chapter=An Introduction to State Space}}. *{{Citation | last1=van der Pol | first1=Balth. | last2=Bremmer | first2=H. | title=Operational calculus | publisher=Chelsea Publishing Co. | location=New York | edition=3rd | isbn=978-0-8284-0327-6 | mr=904873 | year=1987}}. * {{cite book |last1=Rudin |first1=Walter |author1-link=Walter Rudin |title=Real and complex analysis |date=1966 |publisher=McGraw-Hill |location=New York |isbn=0-07-100276-6 |edition=3rd |publication-date=1987 |editor-first=Peter R. |editor-last=Devine}} * {{citation|first=Walter|last=Rudin|author-link=Walter Rudin|title=Functional Analysis|edition=2nd|publisher=McGraw-Hill|year=1991|isbn=978-0-07-054236-5|url-access=registration|url=https://archive.org/details/functionalanalys00rudi}}. * {{citation|first1=Olivier|last1=Vallée|first2=Manuel|last2=Soares|year=2004|title=Airy functions and applications to physics|url=https://books.google.com/books?id=8M42DwAAQBAJ|publisher=Imperial College Press|location=London|isbn=9781911299486}}. *{{Citation|last1=Saichev |first1=A I |last2=Woyczyński |first2=Wojbor Andrzej |title=Distributions in the Physical and Engineering Sciences: Distributional and fractal calculus, integral transforms, and wavelets |year=1997 |isbn=978-0-8176-3924-2 |publisher=Birkhäuser |chapter-url=https://books.google.com/books?id=42I7huO-hiYC&pg=PA3|chapter=Chapter1: Basic definitions and operations }} * {{citation|first=L.|last=Schwartz|author-link=Laurent Schwartz|title=Théorie des distributions|volume=1|publisher=Hermann|year=1950}}. * {{citation|first=L.|last=Schwartz|author-link=Laurent Schwartz|title=Théorie des distributions|volume=2|publisher=Hermann|year=1951}}. * {{citation|first1=Elias|last1=Stein|author-link1=Elias Stein|first2=Guido|last2=Weiss|title=Introduction to Fourier Analysis on Euclidean Spaces|url=https://books.google.com/books?id=xnIwDAAAQBAJ|publisher=Princeton University Press|year=1971|isbn=978-0-691-08078-9}}. * {{citation|first=R.|last=Strichartz|year=1994|author-link=Robert Strichartz|title=A Guide to Distribution Theory and Fourier Transforms|url=https://books.google.com/books?id=T7vEOGGDCh4C|publisher=CRC Press|isbn=978-0-8493-8273-4}}. * {{citation|first=V. S.|last=Vladimirov|title=Equations of mathematical physics|publisher=Marcel Dekker|year=1971|isbn=978-0-8247-1713-1}}. * {{MathWorld|urlname=DeltaFunction|title=Delta Function}} * {{citation|last=Yamashita |first=H. |year=2006 |title= Pointwise analysis of scalar fields: A nonstandard approach |volume=47 |issue =9 |pages=092301|journal=[[Journal of Mathematical Physics]]|doi=10.1063/1.2339017|bibcode = 2006JMP....47i2301Y }} * {{citation|last=Yamashita |first=H. |year=2007 |title= Comment on "Pointwise analysis of scalar fields: A nonstandard approach" [J. Math. Phys. 47, 092301 (2006)] |volume=48 |issue =8 |pages=084101|journal=[[Journal of Mathematical Physics]]|doi=10.1063/1.2771422|bibcode = 2007JMP....48h4101Y |doi-access=free }}
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)