Spectral decomposition and Gelfand’s theorem
نویسندگان
چکیده
منابع مشابه
Spectral decomposition 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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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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ژورنال
عنوان ژورنال: Semigroup Forum
سال: 2009
ISSN: 0037-1912,1432-2137
DOI: 10.1007/s00233-009-9187-4