Green’s Function and Convergence of Fourier Series for Elliptic Differential Operators with Potential from Kato Space
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چکیده
and Applied Analysis 3 for all f ∈ C∞ 0 Ω . Since Aμ A μI is positive for sufficiently large μ it has a positive self-adjoint Friedrichs extension Aμ F such that D (( Aμ ) F ) ⊂ ◦ W m 2 Ω . 1.9 We define the Friedrichs extension of A Aμ − μI to be AF Aμ F − μI such that D AF ⊂ ◦ W m 2 Ω . 1.10 The domain of AF is given by D AF { f ∈ ◦ W m 2 Ω | Af ∈ L2 Ω } . 1.11 It is also well known that this extension has a purely discrete spectrum {λk}k 1 of finite multiplicity having the only one accumulation point at infinity λk → ∞ and a complete orthonormal system {uk x }k 1 of eigenfunctions in L2 Ω . To each function f ∈ L2 Ω we can assign the formal series
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