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Professor Arieh Iserles | Department of Applied Mathematics and…
www.damtp.cam.ac.uk/person/ai1011 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/ai1011 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 | Cantab Capital Institute for the…
www.damtp.cam.ac.uk/research/ccimi/person/ai1011 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. -
Paper2A.dvi
www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_03.pdf30 Nov 2009: In this paper we attempt to apply similar methodology to thecomputation of spectra of highly oscillatory Fredholm operators, of a form ubiquitous in lasertheory. ... It follows readily from standard theory of Fredholm operators (cf. for example -
Publications | Cantab Capital Institute for the Mathematics of…
www.damtp.cam.ac.uk/research/ccimi/publications?page=5811 Jul 2024: 2011). 39,. 2883. (doi: 10.1214/11-aos924). The computation of the spectra of highly oscillatory Fredholm integral operators. -
Publications | Cantab Capital Institute for the Mathematics of…
www.damtp.cam.ac.uk/research/ccimi/publications?page=6911 Jul 2024: 2009). 2,. 1129. (doi: 10.1137/080728548). The spectral problem for a class of highly oscillatory Fredholm integral operators. -
hop07spec.dvi
www.damtp.cam.ac.uk/user/na/NA_papers/NA2008_05.pdf10 Apr 2008: There are two numerical challenges commonly associated with Fredholm operators of thesecond kind. ... This includesthe Li–Fox oscillator (1.5) and other Fredholm operators of relevance in applications. -
Sufficiency of Favard’s condition for a class of band-dominated ...
https://api.newton.ac.uk/website/v0/events/preprints/NI07065its limit operators considered as acting on (Z, U ). Key words: limit operator, Favard condition, Fredholm operator, Wiener algebra. 1 Introduction. ... 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 -
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;. -
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 -
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. -
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). -
Search Publications | Publications
https://publications.maths.cam.ac.uk/publications-search?page=52111 Jul 2024: The computation of the spectra of highly oscillatory Fredholm integral operators. -
Limit Operators, Collective Compactness, and the Spectral Theory of…
https://api.newton.ac.uk/website/v0/events/preprints/NI08017infinite matrices, limit operators, collective compactness, Fredholm. operators, spectral theory. viii. ... Lange and Rabinovich [44], inspired by and building on Muhamadiev’s paper[59], carry the idea of (semi-)Fredholm studies by means of limit -
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: b) Show that an operator is Fredholm if and only if it is invertible modulo thecompact operators. ... c) Show that the Fredholm operators are open in B(H) and that the index isnorm continuous. -
On Spectral Inclusion Sets and Computing theSpectra and Pseudospectra …
www.damtp.cam.ac.uk/research/afha/workshops/cid2014/ChandlerWilde.pdf23 Jul 2014: Fredholm operators. Simon Chandler-Wilde Spectral Inclusion Sets for Spectra and Pseudospectra. ... Fredholm operators. Definition. A : E E is a Fredholm operatorif α := dim(ker A) and β := codim(im A) are both finite.The difference αβ is then called -
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. -
Index theorems for quantum graphs S A Fulling1,2,3, P ...
https://api.newton.ac.uk/website/v0/events/preprints/NI07058index formulas for the exterior-derivative operators A introduced previously. First we need to review the basic notions concerning the Fredholm property and. ... eHm(e) into L2(Γ). All terms in T that involve derivatives of order less than m arecompact -
Taming Discretization Challenges for Nonlinear Eigenvalue Problems
www.damtp.cam.ac.uk/user/mjc249/talks/INI_NEP_mjc.pdf26 Jul 2023: Spess 𝑇 = Sp 𝑇 Spd 𝑇. Most applications of NEPs involve differential operators. ... Comput. Math., 2022.• Webb, Olver, “Spectra of Jacobi operators via connection coefficient matrices,” Commun. -
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. ... P. Nørsett, The computation of the spectra ofhighly oscillatory Fredholm integral operators. -
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: PAPER 10. ANALYSIS OF OPERATORS. Attempt THREE questions. There are EIGHT questions in total. ... 5 Write an essay on the index of Fredholm operators. You should include in youraccount a discussion of Toeplitz operators on the circle. -
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. ... 8 –. 2.3 Fredholm determinant representation of the tau-function. We define the projection operators PΣ, P on the Hilbert space defined in (2.37) in -
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. • -
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: 2. Wiener–Hopf operators. We begin with the proof of Theorem 1.4. ... 11] H. Brunner, A. Iserles, and S. P. Nørsett, The computation of the spectra of highlyoscillatory Fredholm integral operators. -
Spectral theory of large Wiener–Hopf operators with complex-symmetric …
www.damtp.cam.ac.uk/user/na/NA_papers/NA2010_09.pdf12 Nov 2010: Spectral theory of large Wiener–Hopf operators with. complex-symmetric kernels and rational symbols. ... cated Wiener–Hopf integral operators over increasing intervals. The kernel of the operatorsis complex-symmetric and has a rational Fourier -
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. ... ζ H1/2(divΓ, Γ), q H1/2(curlΓ, Γ). Since we aim to apply the powerful Fredholm alternative argument, compactness properties ofthe -
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. ... H =p2. 2m+. 12mω2x2,. in terms of creation and annihilation operators, defined by. -
Pseudoergodic operators and periodic boundary conditions
www.damtp.cam.ac.uk/user/mjc249/pdfs/Pseudoergodic_BCs.pdf22 Jul 2022: not {0}.Second, it is also clear that such operators must be bounded for any d. ... We have now shown why periodic boundary conditions are a natural choice forpseudoergodic operators. -
ON EXISTENCE OF NON-SINGULAR, VACUUM,STATIONARY SPACE-TIMES WITH A…
https://api.newton.ac.uk/website/v0/events/preprints/NI05088Dimensional reduction” of some operators 17A.1. Lichnerowicz Laplacian on two-tensor for a warped product. ... 18. J.M. Lee, Fredholm operators and Einstein metrics on conformally compact manifolds,Memoirs AMS, in press, math.DG/0105046. -
GREEN’S FUNCTION ASYMPTOTICS NEAR THE INTERNALEDGES OF SPECTRA OF ...
https://api.newton.ac.uk/website/v0/events/preprints/NI15041GREEN’S FUNCTION ASYMPTOTICS NEAR THE INTERNALEDGES OF SPECTRA OF PERIODIC ELLIPTIC OPERATORS. ... It is required only that the operators L(k) = L(x,D k) :H2(T) L2(T) are Fredholm for k Cd. -
Riemann-Hilbert problems, Toeplitz operators and ergosurfaces M.…
https://api.newton.ac.uk/website/v0/events/preprints/NI23031Riemann-Hilbert problems, Toeplitz operators. and ergosurfaces. M. Cristina Câmara and Gabriel Lopes Cardoso. ... The previous results can be reformulated in terms of Toeplitz operators as follows. -
COMPUTING SPECTRA – ON THE SOLVABILITY COMPLEXITY INDEX HIERARCHYAND…
www.damtp.cam.ac.uk/research/afha/anders/SCI_FINAL.pdf20 Nov 2023: For A , where is an appropriate domain of operators, we define theproblem functions. ... Given the different domains, we can now state the main theorem for bounded operators. -
Foli_final.dvi
www.damtp.cam.ac.uk/user/na/NA_papers/NA2010_03.pdf17 Mar 2010: Widom, Two remarks on spectral approximations forWiener–Hopf operators. J. Integral Equations Appl. ... P. Nørsett, The computation of the spectra ofhighly oscillatory Fredholm integral operators. -
Spectral computation of highly oscillatory integral equations in…
www.damtp.cam.ac.uk/user/na/NA_papers/NA2018_04.pdf2 Nov 2018: 2011), ‘The computation of the spectra of highly. oscillatory Fredholm integral operators’, J. -
MATHEMATICAL TRIPOS Part II 2002 List of Courses Geometry ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2002/list_II.pdf17 Jun 2019: eiu2du =. πeiπ/4.]. Part II 2002. 26. A3/17 Mathematical Methods. (i) State the Fredholm alternative for Fredholm integral equations of the second kind. -
AN OVERVIEW OF PERIODIC ELLIPTICOPERATORS PETER KUCHMENT Dedicated to …
https://api.newton.ac.uk/website/v0/events/preprints/NI15051AN OVERVIEW OF PERIODIC ELLIPTIC OPERATORS 15. Figure 9. Lattices and fundamental domains (shaded). ... differential operators (ΨDOs) (see [171] and [261]). 4. Floquet transform and direct integral decomposition. -
Geometric inverse problems with emphasis on two dimensions Gabriel ...
https://www.dpmms.cam.ac.uk/~gpp24/GIP2D_driver.pdf1 Feb 2023: with prescribed zero Fourier modes. Chapter 99 discusses inversion formulas up to a Fredholm error and the. ... The theory of pseudodifferential operators (i.e. microlocal anal-ysis) then immediately yields that the singularities of f are uniquely. -
COMPUTING SPECTRA - ON THE SOLVABILITY COMPLEXITY INDEX HIERARCHYAND…
www.damtp.cam.ac.uk/user/mjc249/pdfs/SolvabilityMJC.pdf15 Jun 2020: The new lower bounds demonstrate that the finite section method for compact operators isoptimal. ... Remark 2.5 (The solutions to the computational spectral problem for Schrödinger operators). -
MATHEMATICAL TRIPOS Part II List of Courses Geometry of ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2001/list_II.pdf17 Jun 2019: ii) The Lie algebra su(2) of generators of SU(2) is spanned by the operators{J+,J,J3} satisfying the commutator algebra [J+,J] = 2J3 and [J3,J] = J. -
Complexity Issues in Computing Spectra, Pseudospectra and Resolvents…
www.damtp.cam.ac.uk/research/afha/anders/Banach_Hansen_Nevanlinna_edit2.pdf22 Oct 2016: We then discuss compact operators and show thatthe spectrum can be computed using algorithms with index 1. ... We omitthe details. This gives us the obvious corollary for operators on finite dimensional Hilbert spaces.
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