If and are two families of unitary bases for , and is a fixed number, let and be subspaces of spanned by vectors in and respectively. We study the angle between and as goes to infinity. We show that when and arise in certain arithmetically defined families, the angles between and may either tend to or be bounded away from zero, depending on the behavior of an associated eigenvalue problem.
Pour et deux familles de bases de , et un nombre fixe, nous considérons et deux sous-espaces engendrés par vecteurs de et respectivement. Nous étudions l’angle entre et quand tend vers l’infini. Nous démontrons que, quand et sont présents dans certaines familles définies arithmétiquement, l’angle entre et peut soit tendre vers 0, soit être minoré par une constante strictement positive. Ce comportement dépend d’un problème de valeur propre associé.
@article{AIF_1987__37_1_175_0, author = {Brooks, Robert}, title = {On the angles between certain arithmetically defined subspaces of ${\bf C}^n$}, journal = {Annales de l'Institut Fourier}, pages = {175--185}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {37}, number = {1}, year = {1987}, doi = {10.5802/aif.1081}, mrnumber = {89h:11022}, zbl = {0611.15003}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1081/} }
TY - JOUR AU - Brooks, Robert TI - On the angles between certain arithmetically defined subspaces of ${\bf C}^n$ JO - Annales de l'Institut Fourier PY - 1987 SP - 175 EP - 185 VL - 37 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1081/ DO - 10.5802/aif.1081 LA - en ID - AIF_1987__37_1_175_0 ER -
%0 Journal Article %A Brooks, Robert %T On the angles between certain arithmetically defined subspaces of ${\bf C}^n$ %J Annales de l'Institut Fourier %D 1987 %P 175-185 %V 37 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1081/ %R 10.5802/aif.1081 %G en %F AIF_1987__37_1_175_0
Brooks, Robert. On the angles between certain arithmetically defined subspaces of ${\bf C}^n$. Annales de l'Institut Fourier, Volume 37 (1987) no. 1, pp. 175-185. doi : 10.5802/aif.1081. http://www.numdam.org/articles/10.5802/aif.1081/
[1] The Bottom of the Spectrum of a Riemannian Covering, Crelles J., 357 (1985), 101-114. | MR | Zbl
,[2] The Spectral Geometry of the Apollonian Packing, Comm. P. Appl. Math., XXXVIII (1985), 357-366. | Zbl
,[3] The Spectral Geometry of a Tower of Coverings, J. Diff. Geom., 23 (1986), 97-107. | MR | Zbl
,[4] Representation Theory and Automorphic Functions, W.B. Saunders Co., 1969. | MR | Zbl
, and ,[5] Past and Future, Math. Scand., 21 (1967), 5-16. | MR | Zbl
and ,[6] On the Estimation of Fourier Coefficients of Modular Forms, Proc. Symp. Pure Math, VIII (1965), 1-15. | MR | Zbl
,[7] On Some Exponential Sums, Proc. Nat. Acad. Sci. USA, 34 (1948), 204-207. | MR | Zbl
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