Sentence examples for bounded operator defined on from inspiring English sources

In Section 4, we discuss the existence of almost automorphic solutions of nonlinear difference equations of the form, where is a bounded operator defined on a Banach space.

The matrices are linear bounded operators defined on the Hilbert space (R^{n}).

Let T and (T_{N} ) be linear bounded operator defined by (7) and (12), respectively.

where A is a n × n matrix defined on some interval I ⊂ R, F is a n × 1 vector which is continuous on I × S, S ⊂ R n, T is a bounded linear operator defined on the space of bounded and continuous R n -valued functions on I and r is a n × 1 vector in R n. Existence and uniqueness theorems of the solutions of the problem (1), (2) have been obtained in many papers.

where is a bounded linear operator defined on a Banach space and.

where is a matrix or, more generally, a bounded linear operator defined on a Banach space and is in.

Let 1 ≤ p < ∞, and let T be a bounded linear operator defined on a Krein space K.

Since (P_{Lambda }) is a space of finite dimension d, the semigroup (V^{P}(t)) is uniformly continuous and (A_{V}^{P}) is a bounded linear operator defined on (P_{Lambda }).

Given a bounded linear operator defined on and a discrete almost automorphic function, we give criteria for the existence of discrete almost automorphic solutions of the linear difference equation.

Let A be a bounded self-adjoint operator defined on ({mathcal{H}}).

Indeed, their semigroups and the contraction are self-mappings defined on a closed convex subset C of the Hilbert space H, while the strongly positive linear bounded operator is defined on H.