Analytic and Gevery Class semigroups Generated by −A + iB, and Applications
Angelo Favini, Roberto Triggiani · 2020
Throughout this note, unless otherwise stated, X is a complex Hilbert space with inner product (,) and norm ∥ ∥. We consider the (linear) dissipative operator ( 1.1 ) G = − A + iB ; X ⊃ D ( G ) = D ( A ) ∩ D ( B ) → X , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072102/f87daaca-b142-40c8-8125-02f3c069b4a0/content/eq744.tif"/> D ( A ) ∩ D ( B ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072102/f87daaca-b142-40c8-8125-02f3c069b4a0/content/eq745.tif"/> being dense in X, under the following standing assumptions: H.1 A: X ⊃ D ( A ) → X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072102/f87daaca-b142-40c8-8125-02f3c069b4a0/content/eq746.tif"/> is a (strictly) positive self-adjoint operator on X; H.2 B : X ⊃ D ( B ) → X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072102/f87daaca-b142-40c8-8125-02f3c069b4a0/content/eq747.tif"/> is a self-adjoint operator on X.