A New Algebra of Periodic Generalized Functions
Copyright policy )A New Algebra of Periodic Generalized Functions
Let n denote a strictly positive integer. We construct a complex differential algebra \mathcal G_n of so-called 2\pi -periodic generalized functions. We show that the space \mathcal D^{'(n)}_{2\pi} of 2\pi -periodic distributions on \mathbb R^n can be canonically embedded into \mathcal G_n . Next we lay the foundation for calculation in \mathcal G_n . This algebra \mathcal G_n enables one to solve, in a canonical way, differential problems with strong singular periodic data which have no solution in \mathcal D^{'(n)}_{2\pi} .
Fourier series and coefficients in several variables, Topological linear spaces of test functions, distributions and ultradistributions, Generalized solutions to partial differential equations, complex differential algebra, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Fourier coefficients, [MATH] Mathematics [math], Operations with distributions and generalized functions, differential problems with strong nonlinearities, periodic distributions, Colombeau algebras, \(2\pi\)-periodic generalized functions
Fourier series and coefficients in several variables, Topological linear spaces of test functions, distributions and ultradistributions, Generalized solutions to partial differential equations, complex differential algebra, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Fourier coefficients, [MATH] Mathematics [math], Operations with distributions and generalized functions, differential problems with strong nonlinearities, periodic distributions, Colombeau algebras, \(2\pi\)-periodic generalized functions
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