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SPACES OPERATORS AND TRANSFORMS
FLOQUET THEORY FOR HYPOELLIPTIC EQUATIONS
PROPERTIES OF SOLUTIONS OF PERIODIC EQUATIONS
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1-periodic algebra analogous analytic subset assume Banach bundles Banach space belongs Bloch solution Bloch variety boundary bounded chapter compact complex constant coefficient convergence corollary corresponding define definition differential operator dim Ker domain Due to theorem eigenvalue elliptic equations elliptic operators embedding English transl entire function equivalent estimate exists exponential fiber Floquet exponents Floquet solutions Floquet theory Fourier transform Frechet space Fredholm morphism Fredholm operator Hence Hilbert space holomorphic functions hypoelliptic invertible isomorphism kernel lemma Let us consider Let us denote mapping matrix morphism multiplication neighborhood non-zero norm obtain obviously operator function parabolic partial differential equations periodic coefficients perturbation polynomial proof of theorem proved quasimomentums respect Russian satisfies scalar Schrodinger operator sequence sheaf smooth solvability spectrum statement Stein manifold subbundle subspace surjective topology trivial bundle values vector bundle zero