This page contains a list of user images about Walter Rudin which are relevant to the point and besides images, you can also use the tabs in the bottom to browse Walter Rudin news, videos, wiki information, tweets, documents and weblinks.
Walter Rudin Images
Music video by Rihanna performing Rehab. YouTube view counts pre-VEVO: 19591123. (C) 2007 The Island Def Jam Music Group.
Go to RoosterTeeth.com for all of season 8 of RvB!
The Otherside Remix Music Video was filmed in various locations for about a year and a half throughout 2010-2011. It is the duo's second video collaboration ...
Download This Song: http://bit.ly/KzLBGB Click to Tweet this Vid-ee-oh! http://bit.ly/Nt9lg8 Hi. My name is Nice Peter, and this is EpicLLOYD, and this is th...
Macklemore & Ryan Lewis present the official music video for Can't Hold Us feat. Ray Dalton. Can't Hold Us on iTunes: https://itunes.apple.com/us/album/cant-...
This video accidentally turned out kind of sad, ME SO SOWWY IT NOT POSED TO BE SAD WHO WANTS HUGS AND COOKIES? Also, FYI for anyone attempting this, it takes...
Buy at iTunes: http://goo.gl/zv4o9. New album on sale now! http://turtleneckandchain.com.
So i was pretty hesitant to make this video... but after all of your request, here is my Draw My Life video! Check out my 2nd Channel for more vlogs: http://...
A substitute teacher from the inner city refuses to be messed with while taking attendance.
download this song: http://bit.ly/ERB17 click to tweet this vid-ee-oh! http://clicktotweet.com/vCJ_8 This. Is. Merchandise: http://bit.ly/ERBMerch Hi. My nam...
Buy on iTunes: http://www.Smarturl.it/TTT Amazon: http://idj.to/svJVGM Music video by Rihanna performing Where Have You Been. ©: The Island Def Jam Music Group.
See Harrison Ford in 42! Go to http://42movie.warnerbros.com/ Jimmy Kimmel Live - Harrison Ford Won't Answer Star Wars Questions Jimmy Kimmel Live's YouTube ...
May 2, 1921|
|Died||May 20, 2010(aged 89)|
|Institutions||Professor Emeritus, University of Wisconsin-Madison|
|Alma mater||Duke University (B.A. 1947, Ph.D. 1949)|
|Doctoral advisor||John Jay Gergen|
|Doctoral students||Charles Dunkl|
|Known for||Mathematics textbooks; contributions to harmonic analysis and complex analysis|
|Notable awards||American Mathematical Society Leroy P. Steele Prize for Mathematical Exposition|
He is known for three books on mathematical analysis: Principles of Mathematical Analysis, Real and Complex Analysis, and Functional Analysis. The first (affectionately referred to as "Baby Rudin") was written when Rudin was a Moore instructor at MIT for his undergraduate analysis course and is widely used as a textbook for undergraduate courses in analysis.
Rudin was born into a Jewish family in Austria in 1921. They fled to France after the Anschluss in 1938. When France surrendered to Germany in 1940, Rudin fled to England and served in the British navy for the rest of the war. After the war he left for the United States, and earned his B.A. from Duke University in North Carolina in 1947, and two years later earned a Ph.D. from the same institution. After that he was a C.L.E. Moore instructor at MIT, briefly taught in the University of Rochester, before becoming a professor at the University of Wisconsin–Madison. He remained at the University for 32 years. His research interests spanned from harmonic analysis to complex analysis. He received an honorary degree from the University of Vienna in 2006. His Erdős number is 2.
In 1953, he married fellow mathematician Mary Ellen Estill. The two resided in Madison, Wisconsin, in the eponymous Walter Rudin House, a home designed by architect Frank Lloyd Wright. They had four children.
In this article, Rudin aims to determine under which conditions a given series of spherical surface harmonics is a Laplace series. Uniqueness properties have been studied for a number of orthogonal systems in one variable, with finite ranges of orthogonality, however this paper is one of the first in which the uniqueness problem is considered for a system which is orthogonal over a two-dimensional set.
A Laplace series is a solution to the Laplace equation. This solution is defined as follows:
Important Definitions 
Definition I: The function defined on a set, S, is said to be a spherical surface harmonic of degree n if: is a homogeneous harmonic polynomial in .
Definition II: We say that the series of a spherical surface harmonics is of class K if the series is the Laplace series of a function continuous on S.
Definition III: Suppose the series is of class K. Let be the continuous function whose Laplace series is .
Definition IV: Given the series , define the functions and
Definition V: A closed set Z on S is said to be of capacity zero on S if Z is a proper subset of S and if the stereographic image of Z in a tangent plane, with center of projection in S - Z, is a plane set of capacity zero.
Statement of Main Results 
The main results of Rudin's dissertation are summarized in two theorems and a few corollaries, given below:
Theorem I: Given a series of spherical surface harmonics, , let Z be a closed set of capacity zero on S and suppose:
(i) the given series is of class K
(ii) and are finite on S-Z where is the continuous function whose Laplace series is given by
Theorem II: Given a series of spherical surface harmonics, , having and upper and lower Poisson sums, respectively, and let Z be a closed set of capacity zero. Suppose
(i) the given series is of class K
(ii) and are finite on S-Z
(iii) there exists a function defined on S, on S, such that for P on S
Then the given series is Poisson summable almost everywhere on S and is the Laplace series of its Poisson sum.
Corollary I: If the series is of class K and is summable to zero on S, except possibly on a closed set of capacity zero, then the series vanishes identically.
Corollary II: If the two series, and are of class K and if they are summable to the same function (where it is not necessary that on S) except possibly on a closed set of capacity zero, then the two series are identical.
Other Articles 
- "Uniqueness theory for Laplace series". Trans. Amer. Math. Soc. 68 (2): 287–303. 1950. MR 0033368.
- "Factorization in the group algebra of the real line". Proc Natl Acad Sci U S A 43 (4): 339–340. 1957. PMC 528447.
- "Zero-sets in polydiscs". Bull. Amer. Math. Soc. 73 (4): 580–583. 1967. MR 210934.
- "Holomorphic maps that extend to automorphisms of a ball". Proc. Amer. Math. Soc. 81 (3): 429–432. 1981. MR 597656.
- "Totally real Klein bottles in ". Proc. Amer. Math. Soc. 82 (4): 653–654. 1981. MR 614897.
Major awards 
- Principles of Mathematical Analysis
- Real and Complex Analysis
- Functional Analysis
- Fourier Analysis on Groups
- Function Theory in Polydiscs
- Function Theory in the Unit Ball of Cn
- The Way I Remember It (autobiography, 1991)
See also 
- "Vilas Professor Emeritus Walter Rudin died after a long illness on May 20, 2010".
- Ziff, Deborah (May 21, 2010). "Noted UW-Madison mathematician Rudin dies at 89". Wisconsin State Journal. Retrieved May 21, 2010.
- Rudin, Walter (1950). Uniqueness Theory for Laplace Series (Ph.D.). Duke University.
- "Web of Science". 4/8/13.
- Victor L. Shapiro (1968). "Review: Walter Rudin, Real and complex analysis". Bull. Am. Math. Soc. 74 (1): 79–83.
- J.-P. Kahane (1964). "Review: Walter Rudin, Fourier analysis on groups". Bull. Am. Math. Soc. 70 (2): 230–232.
- Steven G. Krantz (1981). "Review: Walter Rudin, Function theory in the unit ball of Cn". Bull. Am. Math. Soc. (N. S.) 5 (3): 331–339.
- UW Mathematics Dept obituary
- MathDL obituary
- Walter Rudin at the Mathematics Genealogy Project
- Photos of Rudin Residence