I want them to be definite, self-sufficient, and true in what they represent, like expressionist paintings.
where A and B are commuting positive definite self-adjoint operators on a Hilbert space.
Nevertheless, the quantum formulation of the theory yields a manifestly positive definite self-adjoint operator.
Then, for any u ∈ D ( A ), A u = f and A is a positive definite self-adjoint operator.
was studied, where (A D(A)subset Hrightarrow H) is a positive definite self-adjoint operator and A has compact resolvent.
Corollary 1 Let A be a positive definite self-adjoint operator in Hilbert space H and it have compact resolvent, f: J × H → H be continuous.
Theorem 1 Let A be a positive definite self-adjoint operator in Hilbert space H and it have compact resolvent, f: J × H → H be continuous.
We consider the problem (1) under the assumption that A is a positive definite self-adjoint operator with A ≥ δ I, where δ > δ 0 > 0. Theorem 1 [4].
Let H be a separable Hilbert space with scalar product ((x,y)), (x,yin H), and A be a positive definite self-adjoint operator in H ((A=A^ ge cE), (c>0), E is the identity operator).
Since the positive definite self-adjoint operator A has compact resolvent, the embedding D(A) ↪ H is compact, and therefore T (t)(t ≥ 0) is also a compact semigroup.
where A and B are commuting positive definite self-adjoint operators on a Hilbert space, with upper and lower bounds M i and m i, i = 1, 2, respectively.
