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58G25 — 2 results found.

      
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Invariant Operators with Complex Potentials
C. R. Math. Rep. Acad. Sci. Canada Vol. 33 (4) 2011, pp. 107–115
H.D. Fegan; B. Steer (Received: 2011/02/16)

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For an operator \(D\) a potential \(Q\) is null isospectral if \(\operatorname{Spec}(D+Q) = \operatorname{Spec}(D)\). In this paper we study bundle maps \(Q\) on a homogeneous vector bundle over a homogeneous space that are null isospectral potentials for a large class of invariant operators \(D\), including elliptic self-adjoint differential operators. This result includes and generalizes previous results where \(D\) is the Laplace operator and \(Q\) is a complex valued function rather than a bundle map. To illustrate these results we give the examples of the Laplace and Dirac operators on \(S^1\).

Soit \(\Delta\) l’opérateur de Laplace sur une variété différentiable homogène compacte. On sait qu’il existe des fonctions \(Q\) non-nulles à valeurs complexes telles que \(\Delta\) et \(\Delta+Q\) ont le même spectre. Nous montrons ici que ce résultat s’étend largement. Si \(D\) désigne un opérateur elliptique invariant et auto-adjoint opérant sur les fonctions à valeurs dans un fibré vectoriel complexe homogène \(\mathbf{E}\) il exist des fonctions \(Q\) non-nulles à valeurs dans le fibré \(\operatorname{End}(\mathbf{E})\) telles que \(D\) et \(D+Q\) ont le même spectre. Les fonctions \(Q\) possibles se laissent calculer facilement dans le cas de \(S^1\) et l’opérateur de Dirac.

Spectral rigidity of Hopf surfaces
C. R. Math. Rep. Acad. Sci. Canada Vol. 15 (4) 1993, pp. 131–136
D. Perrone (Received: 1993/03/31, Revised: 1993/06/07)

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algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup cycles of ideals elliptic curves fixed point Fourier transform function fields. general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping noninterlacing numerical range orthogonal polynomials Predual space prime number property SP quadratic forms Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces Weak Markov set Whitney problems

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05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F20 37F25 39B72 42C05 43A07 43A62 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 60J75 83C05

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