2011/02/19 by V. N. Tibabishev, Tibabishev, V. N.
Mathematics · #42A38 (Secondary) #43A85 #62M10 (Primary) #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #FOS: Mathematics #General Mathematics (math.GM) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1102.3983
openalex publication_date 2011/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of determining the Fourier integral in the Hilbert space of square integrable functions. Fourier integral is the scalar product of two functions belonging to the Hilbert space of square integrable functions and the Hilbert space of almost periodic functions. Scalar product for different Hilbert spaces defined at the intersection of these spaces, which contains only one zero element. Therefore, the Fourier integral is not defined in the Hilbert space of square integrable functions with nonzero norm.