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Professor Arieh Iserles | Faculty of Mathematics
https://www.maths.cam.ac.uk/person/ai106 Jul 2024: the solution of rapidly oscillating ordinary differential equations, computation of spectra of Fredholm operators with highly oscillatory kernels and rapid approximation of functions by Birkhoff series. -
MATHEMATICAL TRIPOS Part III Friday, 3 June, 2011 1:30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2011/paper_15.pdf30 Aug 2019: Part III, Paper 15. 3. 3. (i) Define Fredholm map, Fredholm operator, Fredholm index. ... iii) Prove that s As is Fredholm.[You may quote the Closed Range Lemma without proof]. -
MATHEMATICAL TRIPOS Part II Alternative B Thursday 6 June ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2002/PaperIIB_4.pdf17 Jun 2019: Define a Fredholm operator T , on a Hilbert space H, and define the index of T. ... not using anytheorems about Fredholm operators) that, for each k Z, there is a Fredholm operator Son H with ind S = k. -
MATHEMATICAL TRIPOS Part III Friday, 5 June, 2009 9:00 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2009/Paper8.pdf30 Aug 2019: 2. 1. (a) Define what is meant by a Fredholm operator of index n on Hilbert space. ... b) Show that an operator is Fredholm if and only if it is invertible modulo thecompact operators. -
MATHEMATICAL TRIPOS Part II Alternative B Wednesday 6 June ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2001/PaperIIB_3.pdf17 Jun 2019: Define what it meansto say that T is (i) compact, and (ii) Fredholm. ... Prove that S and T are Fredholm ifand only if both ST and T S are Fredholm. -
MATHEMATICAL TRIPOS Part III Friday 3 June, 2005 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2005/Paper29.pdf30 Aug 2019: 3 Using Mahler’s method, show that the Fredholm series. n=0 zln , where l is an. ... Prove that, for l > 3 and z = 12 , the transcendence of the Fredholm series can beobtained directly from the Thue-Siegel-Roth theorem. -
MATHEMATICAL TRIPOS Part IB Tuesday, 2 June, 2015 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2015/PaperIB_1.pdf17 Jun 2019: Show that theSturm–Liouville equation can be written as a so-called Fredholm integral equation of theform. ... iv) Derive the Fredholm integral equation for the Sturm–Liouville equation on theinterval [0,1]. -
MATHEMATICAL TRIPOS Part III Wednesday, 6 June, 2012 1:30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2012/paper_7.pdf30 Aug 2019: range(L) is closed. A complex number ξ is said to in the essential spectrum of L iff (L ξ) is not Fredholm. ... Prove that L isFredholm iff L K is Fredholm. (g) Consider a bounded operator L and a compact operator K on H. -
MATHEMATICAL TRIPOS Part II Alternative A Wednesday 5 June ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2002/PaperIIA_3.pdf17 Jun 2019: 17C Mathematical Methods. (i) State the Fredholm alternative for Fredholm integral equations of the second kind. -
MATHEMATICAL TRIPOS Part III Thursday 31 May 2007 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2007/Paper10.pdf30 Aug 2019: 5 Write an essay on the index of Fredholm operators. You should include in youraccount a discussion of Toeplitz operators on the circle.
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