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Algebra --- Matrices --- Differential equations --- Eigenvalues --- Formes normales (mathématiques) --- Normal forms (Mathematics) --- Formes normales (mathématiques) --- Equations differentielles --- Stabilite

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519.6 --- 681.3*G13 --- 681.3*G4 --- 681.3*G4 Mathematical software: algorithm analysis certification and testing efficiency portability reliability and robustness verification --- Mathematical software: algorithm analysis certification and testing efficiency portability reliability and robustness verification --- 681.3*G13 Numerical linear algebra: conditioning determinants Eigenvalues error analysis linear systems matrix inversion pseudoinverses sparse and very largesystems --- Numerical linear algebra: conditioning determinants Eigenvalues error analysis linear systems matrix inversion pseudoinverses sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- 681.3*G4 Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.614 --- 629.78 --- #TELE:d.d. Prof. A. J. J. Oosterlinck --- 681.3*F1 --- 681.3*F21 --- 681.3*F1 Computation by abstract devices --- Computation by abstract devices --- 519.614 Numerical methods for computing eigenvalues and eigenvectors of matrices --- Numerical methods for computing eigenvalues and eigenvectors of matrices --- 681.3*F21 Numerical algorithms and problems: computation of transforms; computations infinite fields; computations on matrices; computations on polynomials; numer-theoretic computations--See also {681.3*G1}; {681.3*G4}; {681.3*I1} --- Numerical algorithms and problems: computation of transforms; computations infinite fields; computations on matrices; computations on polynomials; numer-theoretic computations--See also {681.3*G1}; {681.3*G4}; {681.3*I1} --- Ruimteschip --- Programming --- Numerical solutions of algebraic equations --- EISPACK (Computer program) --- Langages de programmation --- Programming languages (Electronic computers) --- Langages de programmation.

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Mathematical control systems --- Numerical analysis --- Planning (firm) --- System analysis --- Equations, Simultaneous --- Sparse matrices --- Data processing. --- -Sparse matrices --- -System analysis --- -519.6 --- 681.3*G13 --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Spare matrix techniques --- Matrices --- Simultaneous equations --- Data processing --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Analyse de systèmes --- Matrices éparses --- Informatique --- Matrices éparses --- 519.6 --- Matrices éparses.

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Algebra --- Matrix inversion --- Pseudoinverses --- Congresses --- -Pseudoinverses --- -512.64 --- 519.6 --- 681.3*G13 --- Algebras, Linear --- Numerical analysis --- Inverse matrices --- Inverse of a matrix --- Inversion, Matrix --- Linear operators --- Matrices --- Linear and multilinear algebra. Matrix theory --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Generalized inverses --- Congresses. --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 512.64 Linear and multilinear algebra. Matrix theory --- 512.64 --- Pseudo-inverses --- Opérateurs linéaires --- Inverses généralisés --- Inverses généralisés. --- Matrix inversion - Congresses --- Pseudoinverses - Congresses --- Opérateurs linéaires --- Inverses généralisés.

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The application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the results of that work in the form of new or more straightforward treatments of the spectral theory of the Laplace-Beltrami operator over fundamental domains of finite area; the meromorphic character over the whole complex plane of the Eisenstein series; and the Selberg trace formula.CONTENTS: 1. Introduction. 2. An abstract scattering theory. 3. A modified theory for second order equations with an indefinite energy form. 4. The Laplace-Beltrami operator for the modular group. 5. The automorphic wave equation. 6. Incoming and outgoing subspaces for the automorphic wave equations. 7. The scattering matrix for the automorphic wave equation. 8. The general case. 9. The Selberg trace formula.

Harmonic analysis. Fourier analysis --- Automorphic functions --- Scattering (Mathematics) --- Fonctions automorphes --- Dispersion (Mathématiques) --- Automorphic functions. --- Scattering (Mathematics). --- Dispersion (Mathématiques) --- Selberg, Formule de trace de --- Selberg trace formula --- Eisenstein series --- Eisenstein, Séries d' --- Scattering theory (Mathematics) --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Fuchsian functions --- Functions, Automorphic --- Functions, Fuchsian --- Functions of several complex variables --- Absolute continuity. --- Algebra. --- Analytic continuation. --- Analytic function. --- Annulus (mathematics). --- Asymptotic distribution. --- Automorphic function. --- Bilinear form. --- Boundary (topology). --- Boundary value problem. --- Bounded operator. --- Calculation. --- Cauchy sequence. --- Change of variables. --- Complex plane. --- Conjugacy class. --- Convolution. --- Cusp neighborhood. --- Cyclic group. --- Derivative. --- Differential equation. --- Differential operator. --- Dimension (vector space). --- Dimensional analysis. --- Dirichlet integral. --- Dirichlet series. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Eisenstein series. --- Elliptic operator. --- Elliptic partial differential equation. --- Equation. --- Equivalence class. --- Even and odd functions. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Exponential function. --- Fourier transform. --- Function space. --- Functional analysis. --- Functional calculus. --- Fundamental domain. --- Harmonic analysis. --- Hilbert space. --- Hyperbolic partial differential equation. --- Infinitesimal generator (stochastic processes). --- Integral equation. --- Integration by parts. --- Invariant subspace. --- Laplace operator. --- Laplace transform. --- Lebesgue measure. --- Linear differential equation. --- Linear space (geometry). --- Matrix (mathematics). --- Maximum principle. --- Meromorphic function. --- Modular group. --- Neumann boundary condition. --- Norm (mathematics). --- Null vector. --- Number theory. --- Operator theory. --- Orthogonal complement. --- Orthonormal basis. --- Paley–Wiener theorem. --- Partial differential equation. --- Perturbation theory (quantum mechanics). --- Perturbation theory. --- Primitive element (finite field). --- Principal component analysis. --- Projection (linear algebra). --- Quadratic form. --- Removable singularity. --- Representation theorem. --- Resolvent set. --- Riemann hypothesis. --- Riemann surface. --- Riemann zeta function. --- Riesz representation theorem. --- Scatter matrix. --- Scattering theory. --- Schwarz reflection principle. --- Selberg trace formula. --- Self-adjoint. --- Semigroup. --- Sign (mathematics). --- Spectral theory. --- Subgroup. --- Subsequence. --- Summation. --- Support (mathematics). --- Theorem. --- Trace class. --- Trace formula. --- Unitary operator. --- Wave equation. --- Weighted arithmetic mean. --- Winding number. --- Eisenstein, Séries d'. --- Analyse harmonique