You need two additional assumptions: the operator $A$ has to be a so-called cosine function generator, and your product space has to be $V\times H$ with a space $V\subset H$.

Cosine function generator is more than sectorial, it is moreor less when the numerical range of $A$ is in a parabola (selfadjoint negative semidefinite is ok).

The space $V$ is difficult, but if $A$ is selfadjoint, then it is essentially $D(A^{1/2})$.

See Section VI.3 in

Klaus-Jochen Engel and Rainer Nagel, MR 1721989 One-parameter semigroups for linear evolution equations, ISBN: 0-387-98463-1.

or Section 7.4 in

Haase, Markus The functional calculus for sectorial operators. Operator Theory: Advances and Applications, 169. Birkhäuser Verlag, Basel, 2006. xiv+392 pp. ISBN: 978-3-7643-7697-0; 3-7643-7697-X

You need two additional assumptions: the operator $A$ has to be a so-called cosine function generator, and your product space has to be $V\times H$ with a space $V\subset H$.

Cosine function generator is more than sectorial, it is more or less when the numerical range of $A$ is in a parabola (selfadjoint negative definite is ok, this is discussed in the references Liviu mentioned).

The space $V$ is difficult, but if $A$ is selfadjoint, then it is essentially $D(A^{1/2})$.

See Section VI.3 in

Klaus-Jochen Engel and Rainer Nagel, MR 1721989 One-parameter semigroups for linear evolution equations, ISBN: 0-387-98463-1. (here a downloadable version)

or Section 7.4 in

Haase, Markus The functional calculus for sectorial operators. Operator Theory: Advances and Applications, 169. Birkhäuser Verlag, Basel, 2006. xiv+392 pp. ISBN: 978-3-7643-7697-0; 3-7643-7697-X