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Professor Arieh Iserles | Department of Applied Mathematics and…
www.damtp.cam.ac.uk/person/ai1010 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. -
Professor Arieh Iserles | Faculty of Mathematics
https://www.maths.cam.ac.uk/person/ai1010 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. -
Georg Maierhofer - Hooke Research Fellow at the University of Oxford
www.damtp.cam.ac.uk/user/gam37/11 Jun 2024: Analysis of collocation methods for Fredholm integral equations. In collaboration with Prof. ... Convergence analysis of least-squares oversampled collocation methods for Fredholm integral equations. -
Professor Arieh Iserles | Cantab Capital Institute for the…
www.damtp.cam.ac.uk/research/ccimi/person/ai1010 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. -
hop07spec.dvi
www.damtp.cam.ac.uk/user/na/NA_papers/NA2008_05.pdf10 Apr 2008: corresponding to a Fredholm integral operator of rank 2. Its (unique) solution is given by. ... There are two numerical challenges commonly associated with Fredholm operators of thesecond kind. -
Publications | Cantab Capital Institute for the Mathematics of…
www.damtp.cam.ac.uk/research/ccimi/publications?page=5810 Jul 2024: 2011). 1,. 337. (doi: 10.1109/Allerton.2011.6120187). The computation of the spectra of highly oscillatory fredholm integral operators. -
Paper2A.dvi
www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_03.pdf30 Nov 2009: Spectra of highly oscillatory Fredholm integral operators 15. =. 1. 1Pm(x) cos ωxdx. ... Spectra of highly oscillatory Fredholm integral operators 29. 3.5 Large-n asymptotics. -
Publications | Cantab Capital Institute for the Mathematics of…
www.damtp.cam.ac.uk/research/ccimi/publications?page=6910 Jul 2024: doi:The spectral problem for a class of highly oscillatory Fredholm integral operators. -
Video & Audio: A polyfold lab report -…
https://sms.cam.ac.uk/media/2548633I will survey various results on applications and extensions of Hofer-Wysocki-Zehnder's polyfold theory: - fiber products of polyfold Fredholm sections - equivariant transversality - existence and obstructions - equivariant fundamental class - -
Video & Audio: Constructing the virtual …
https://sms.cam.ac.uk/media/2547068Consider a space XX, such as a compact space of JJ-holomorphic stable maps with closed domain, that is the zero set of a Fredholm operator. -
arX iv:2 211. 0113 9v1 [m ath- ph] 2 ...
https://api.newton.ac.uk/website/v0/events/preprints/NI22003regular singularities by using their Fredholm determinant representation [8], and show that they. ... describe the pants decomposition, and briefly recap the construction of the Fredholm deter-. -
Sufficiency of Favard’s condition for a class of band-dominated ...
https://api.newton.ac.uk/website/v0/events/preprints/NI07065v) A is Fredholm on one of the spaces Y. (vi) A is Fredholm on all the spaces Y. ... 17] S. Roch: Band-dominated operators on pspaces: Fredholm indices and finitesections, Acta Sci. -
Numerical analysis preprints, 2001–2010 2010: NA2010/01: Arieh…
www.damtp.cam.ac.uk/user/na/NA_Group/Reports01_10.html26 Jan 2017: NA2009/03: Hermann Brunner, Arieh Iserles & Syvert Nørsett, "The computation of the spectra of highly oscillatory Fredholm integral operators". ... NA2008/05: Hermann Brunner, Arieh Iserles & Syvert Nørsett, "The spectral problem for a class of highly -
Limit Operators, Collective Compactness, and the Spectral Theory of…
https://api.newton.ac.uk/website/v0/events/preprints/NI08017If C is semi-Fredholm then α(C) β(C) is called theindex of C. ... 899) that L is Fredholm iff all the limitoperators of L are invertible. -
Publications: Refereed Journals Jing Gao & Arieh Iserles, "A …
www.damtp.cam.ac.uk/user/na/people/Arieh/Arieh_Iserles/Papers.html22 Feb 2024: H. Brunner, A. Iserles & S. Nørsett, "The computation of the spectra of highly oscillatory Fredholm integral operators", J. ... Nørsett, "The spectral problem for a class of highly oscillatory Fredholm differential equations" IMA J. -
Index theorems for quantum graphs S A Fulling1,2,3, P ...
https://api.newton.ac.uk/website/v0/events/preprints/NI07058of finite rank), then T K is also Fredholm and index(T K) = index T. ... This operator is Fredholm of. index E p. Therefore,index A = E p = E. -
Desargues.dvi
https://api.newton.ac.uk/website/v0/events/preprints/NI09049In particular, we identify the Fredholm deter-minant of the integral equation inverting the nonlocal ̄-dressing problem with the τ -function. ... Then, by the Fredholm alternative, the homogeneousequation with η = 0 has only the trivial solution. -
The Isospectral Dirac Operator on the 4-dimensional Quantum Euclidean …
https://api.newton.ac.uk/website/v0/events/preprints/NI06056the Fredholm module canonically associated to the spectral triple to an ‘instanton’ projection e. ... With different representations a non-trivial Fredholm module was already constructed in [17]. -
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]. -
Arieh Iserles: Research My main research is on various ...
www.damtp.cam.ac.uk/user/na/people/Arieh/Arieh_Iserles/Research.html3 Aug 2016: Spectral theory of highly oscillatory Fredholm operators, e.g. the Fox–Li equation in both its operator-theoretic and computational aspects;. -
Chebyshev polynomial approximations for some hypergeometric systems…
https://api.newton.ac.uk/website/v0/events/preprints/NI09059Juri M. Rappoport 7. equation are present in the form of single quadrature from Fredholm inte-gral equation type. ... It consists of numerical solutionof the second kind Fredholm integral equation with symmetric kernels andthe followed taking of -
TCM Publications in 1997
www.tcm.phy.cam.ac.uk/publications/Pubs1997.html2 Jun 2015: O.F. BANDTLOW, I. ANTONIOU and Z. SUCHANECKI "Resonances of Dynamical Systems and Fredholm-Riesz Operators on Rigged Hilbert Spaces" Computers & Mathematics with Applications 34, 95-102 (1997). -
MAMA/105, NST3AS/105, MAAS/105 MAT3 MATHEMATICAL TRIPOS Part III…
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_105.pdf9 Jul 2024: State the Fredholm Alternative for (†). (ii) Let U = (0,2π) R and define the operator. -
The bead process on the torus - CMIH - The Centre for Mathematical…
https://archive.cmih.maths.cam.ac.uk/events-archive/the-bead-process-on-the-torus/We develop a continuous version of Kasteleyn theory to show that partition functions for bead configurations on T_n may be expressed in terms of Fredholm determinants of certain operators on -
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. -
On Spectral Inclusion Sets and Computing theSpectra and Pseudospectra …
www.damtp.cam.ac.uk/research/afha/workshops/cid2014/ChandlerWilde.pdf23 Jul 2014: specessA = {λ C : AλI not Fredholm on E},specεA = spec A {λ C : ‖(AλI )1‖ > 1/ε}. ... For A L(E ) and ε > 0, we put. spec A = {λ C : AλI not invertible on E},specessA = {λ C : AλI not Fredholm on E},. -
TIME-PERIODIC SOLUTIONS OF ADVECTION-DIFFUSIONEQUATIONS ON MOVING…
https://api.newton.ac.uk/website/v0/events/preprints/NI14053Therefore, our existence proof mainly relies on a simple fixed point iterationand standard Fredholm theory. ... ut. The Fredholm alternative in Proposition 3.3 then gives the main theorem of thepaper. -
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. -
Existence results for the Helmholtz equation in periodic wave-guides…
https://api.newton.ac.uk/website/v0/events/preprints/NI18014MSC: 35J05, 78A40. Keywords: Helmholtz equation, wave-guide, periodic media,Fredholm alternative. 1 Introduction. ... Our result has therefore verymuch the character of a Fredholm alternative: If solutions are unique, then theyexist for arbitrary f. -
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. -
A CONTINUOUS ANALOG OF THE BINARY DARBOUXTRANSFORMATION FOR THE ...
https://api.newton.ac.uk/website/v0/events/preprints/NI22026JR,Jρ. )given by (6.1). Let σ be a (signed). finite measure supported on R+ such that the Fredholm integral equation. ... Thus we arrive at the Fredholm integral equation. y Ky = ψ, (7.17). -
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. -
Stabilized FEM-BEM Coupling for Maxwell Transmission Problems R.…
https://api.newton.ac.uk/website/v0/events/preprints/NI07012Meury 3. Fredholm alternative. To this end, most authors have studied the integral operators intrinsicallyon Γ. ... Fredholm alternative on either smooth or non-smooth domainsand prevents us from establishing existence and uniqueness of solutions and -
HOPreportedited.dvi
https://api.newton.ac.uk/website/v0/events/hop/reports/scientific-reportdress an important and challenging set of problems: computation of Fredholm and Volterra. ... been already noted in the computation of spectra of Fredholm operators. • -
Foli_final.dvi
www.damtp.cam.ac.uk/user/na/NA_papers/NA2010_03.pdf17 Mar 2010: Amer. Math. soc. 130 (2001), 1755–1764. [14] F. J. Dyson, Fredholm determinants and inverse scattering problems. ... Commun.Math. Phys. 47 (1976), 171–183. [15] T. Ehrhardt, Dyson’s constant in the asymptotics of the Fredholm determinantof the sine -
Partial degeneration of finite gap solutions to the Korteweg-deVries…
https://api.newton.ac.uk/website/v0/events/preprints/NI2201318] formula of Fredholm type:. u(x,t) =22x ln det [1N G(x,t)] , where. ... 21], where, however, the author ends up with a different determinantal formula (not a Fredholm determi-. -
Part III Analysis of PDE: Rough syllabus Claude Warnick ...
https://www.dpmms.cam.ac.uk/~cmw50/resources/PartIIIPDE/PDESyllabus.pdf15 Oct 2021: b) Compactness Weak compactness for Hilbert spaces; Rellich-Kondrachov theorem;Fredholm alternative; spectrum of L; spectral theorem for symmetric (formally self-adjoint) elliptic BVPs. -
The Fox–Li operator as a test and a spur ...
www.damtp.cam.ac.uk/user/na/NA_papers/NA2011_06.pdf26 Mar 2011: However, in the case at hand wecan say more. There are explicit formulae for the Fredholm determinants ofWiener–Hopf operators with rational symbols. ... Iserles, and S. P. Nørsett, The spectral problem for a class ofhighly oscillatory Fredholm -
TechReport.dvi
mi.eng.cam.ac.uk/reports/svr-ftp/ng_tr529.pdf21 Apr 2006: We may therefore express the imaging process by the Fredholm integral,. ... x, y, z) = δ (xp) δ (z z0).Expressing the Fredholm integral of Equation 1 in terms of xp and yp, we obtaing (x, y, t) =. h (x′ cos θ y′ -
Notices by Faculty Boards, etc. - Cambridge University Reporter 6203
https://www.reporter.admin.cam.ac.uk/reporter/2010-11/weekly/6203/section5.shtml17 Nov 2010: Iserles. The computation of Fredholm spectra. 62. Jozsa. Classical simulation of quantum computations. -
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]. -
Nick_retirement_conference
www.damtp.cam.ac.uk/user/mjc249/talks/Nick_NEP_mjc.pdf17 Aug 2023: use contour integration to convert to a linear pencil. 14. Technical point: Spd 𝑇 = 𝜆 Sp 𝑇 :𝜆 isolated,𝑇 𝜆 Fredholm , Spess 𝑇 = Sp 𝑇 Spd 𝑇. -
First-order trace formulas for the iterates of theFox–Li operator ...
www.damtp.cam.ac.uk/user/na/NA_papers/NA2010_08.pdf30 Jul 2010: described, then for W(aλ)to be Fredholm it is necessary that |ϕ(ξ)| = O(log |ξ|) as |ξ|. ... 11] H. Brunner, A. Iserles, and S. P. Nørsett, The computation of the spectra of highlyoscillatory Fredholm integral operators. -
J. Fluid Mech. (2018), vol. 850, R1, doi:10.1017/jfm.2018.483…
www.damtp.cam.ac.uk/user/lauga/papers/150.pdf16 Jul 2018: Algebraic SBTs typically representthe flow around a rigid body through a one-dimensional Fredholm equation of thesecond kind. ... Similarly to other SBT treatments,these relationships are either linear or a one-dimensional Fredholm equation of thesecond -
Riemann-Hilbert problems, Toeplitz operators and ergosurfaces M.…
https://api.newton.ac.uk/website/v0/events/preprints/NI23031Indeed, the operator TG is Fredholm,i.e. it has a closed range and finite dimensional kernel and cokernel, if and only if G admitsa WH factorisation; TG is invertible if ... dim kerTG codim ImTG = 0, (17). i.e., the Fredholm index of TG is zero. -
arX iv:1 812. 0442 2v1 [m ath. PR] 11 ...
https://api.newton.ac.uk/website/v0/events/preprints/NI18006dµ(w). In order to manipulate the regularized Fredholm determinant we approximate the right handside by. -
STABILITY OF THE PERIODIC TODA LATTICE UNDER SHORT RANGE ...
https://api.newton.ac.uk/website/v0/events/preprints/NI07032STABILITY OF THE PERIODIC TODA LATTICE. UNDER SHORT RANGE PERTURBATIONS. SPYRIDON KAMVISSIS AND GERALD TESCHL. Abstract. We consider the stability of the periodic Toda lat-tice (and slightly more generally of the algebro-geometric finite-gap lattice) -
Taming Discretization Challenges for Nonlinear Eigenvalue Problems
www.damtp.cam.ac.uk/user/mjc249/talks/INI_NEP_mjc.pdf26 Jul 2023: Sp 𝑇 = 𝜆 Ω: 𝑇 𝜆 is not invertible. Spd 𝑇 = 𝜆 Sp 𝑇 : 𝜆 isolated, 𝑇 𝜆 Fredholm. -
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.
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