The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space

Fourier series is a well-established subject and widely applied in various fields. However, there much less work on double coefficients relation to spaces of general sequences. We understand the space as an abstract sequences examine relationships sequences: p-power summable for p = 1, 2, Hilbert Using uniform convergence sense Cesàro mean, we verify inclusion between four sequences; they are nested proper subsets. The completions two them found be identical equal largest one. prove that two-parameter Wiener isomorphic means associated with coefficients. Furthermore, establish sequence space. think verified at intermediate stage this paper will provide basis structures those expect developed further single-indexed