Spectral decomposition and Gelfand’s theorem
نویسنده
چکیده
In this paper we are interested in spectral decomposition of an unbounded operator with discrete spectrum. We show that if A generates a polynomially bounded n-times integrated group whose spectrum set σ(A) = {iλk; k ∈ Z} is discrete and satisfies ∑ 1 |λk|δ k < ∞ (n and l nonnegative integers), then there exists projectors (Pk)k∈Z∗ such that ∑ Pkx = x (x ∈ D(A)), where δk = min ( |λk+1−λk| 2 , |λk−1−λk| 2 ) . AMS Subject Classifications: Primary 47A60, 47A10, 47D03, 47D06, 47D62. Secondary 47A10.
منابع مشابه
On spectral decomposition of unbounded operators and Gelfand’s theorem
In this paper we are interested in spectral decomposition of an unbounded operator with discrete spectrum. We show that if A generates a polynomially bounded n-times integrated group whose spectrum set σ(A) = {iλk; k ∈ Z } is discrete and satisfies ∑ 1 |λk|δ k < ∞ (n and l nonnegative integers), then there exists projectors (Pk)k∈Z∗ such that ∑ Pkx = x (x ∈ D(A)), where δk = min ( |λk+1 − λk| 2...
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