Geodesic
An Example in the Theory of Bisectorial Operators
Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 249-254

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An unbounded operator is said to be bisectorial if its spectrum is contained in two sectors lying, respectively, in the left and right half-planes and the resolvent decreases at infinity as $1/\lambda$. It is known that, for any bounded function $f$, the equation $u'-Au=f$ with bisectorial operator $A$ has a unique bounded solution $u$, which is the convolution of $f$ with the Green function. An example of a bisectorial operator generating a Green function unbounded at zero is given.
Keywords: bisectorial operator, linear differential equation, Green function, resolvent set, Fourier series. 
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     author = {A. V. Pechkurov},
     title = {An {Example} in the {Theory} of {Bisectorial} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_2_a6/}
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A. V. Pechkurov. An Example in the Theory of Bisectorial Operators. Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 249-254. http://geodesic.mathdoc.fr/item/MZM_2015_97_2_a6/