Spectral methods in infinite-dimensional analysis. 1 (1995)

According algebra arbitrary Assume Berezansky chain Chapter coincides commuting condition consider constructed continuous convergence corresponding countable cylindrical measure cylindrical sets D₁ defined definition Denote dense differential eigenvectors English transl equality Example exists fact finite Fock space follows formula Fourier transform function Gaussian measure given H₁ H₂ Hence Hermite polynomials Hilbert space Ho,k imbedding operator implies inequality infinite-dimensional integral introduce isomorphism joint RI Ker Q kernel L₁ L₂ Lemma linear linear span mapping Math measure Ys nonnegative norm nuclear rigging nuclear space o-algebra obtain orthogonal orthonormal basis polynomials pr lim projective limit Proof prove quasinuclear R₂ representation respect scalar product Section selfadjoint selfadjoint operators sequence space H spectral spectral theorem Subsection subspace supp tensor product Theorem topological space topology Ukrain vector virtue Y₁