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## Main Question or Discussion Point

What is the vector space under consideration when we say that a linear differential equation is of the form

[tex] Dy=f [/tex]

where the differential operator D is a linear operator? What is its underlying field?

Also, is the Fourier series just an expansion (for a subspace of this vector space) in the "sine and cosine basis"?

[tex] Dy=f [/tex]

where the differential operator D is a linear operator? What is its underlying field?

Also, is the Fourier series just an expansion (for a subspace of this vector space) in the "sine and cosine basis"?