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analytic assume bifurcation bounded Cauchy problem coefficients cohomology Communicated by Kosaku Communicated by Kunihiko compact complex condition converges convex Corollary cusp forms defined denote Department of Mathematics DG algebra diffeomorphisms differential equations differential operator eigenvalue elements elliptic Emeritus Professor Enriques surface equivalent exists finite Fourier series function Hatada Hecke operators Hence Holonomic Quantum Fields homomorphism implies induced isomorphism Japan Acad Jimbo Kisaburo Yokota Kiyoo Wadati Kosaku Yosida Kunihiko Kodaira Kyoto University Lemma Lie algebra linear manifold mapping Math matrix Michio Jimbo Mikio Sato nonlinear norm notation obtain partial isometry periodic polynomial positive constant prime Proc Proof of Theorem Proposition prove rational integer real numbers Remark resp respectively satisfies Sato sity of Tokyo spectral sequence stable Steenrod operations Studies on Holonomic subgroup subset subspace surjective tangent bundle tion topological transform unique vector fields weakly