On the Operator $\circledast^{k}$ Related to Heat Equation

On the Operator k Related to Heat Equation

On the operator ⊕k related to the wave equation and Laplacian

In this paper, we study the Green function of the operator ♦m ,iterated k-times and is defined by

A solution of an operator equation related to the KdV equation

For a given nonzero bounded linear operator A on a Banach space X, we show that if A or A∗ has an eigenvalue then, except when the dimension of X is equal to two and the trace of A is zero, there exists a bounded linear operator B on X such that (i) AB + BA is of rank one, and (ii) I + f (A)B is invertible for every function f analytic in a neighborhood of the spectrum of A. This result was mot...

The solutions to the operator equation $TXS^* -SX^*T^*=A$ in Hilbert $C^*$-modules

In this paper, we find explicit solution to the operator equation $TXS^* -SX^*T^*=A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $T,S$ have closed ranges and $S$ is a self adjoint operator.

The Heat Equation for the Hermite Operator on the Heisenberg Group∗

We give a formula for the one-parameter strongly continuous semigroup e−tL, t > 0, generated by the Hermite operator L on the Heisenberg group H1 in terms of Weyl transforms, and use it to obtain an L2 estimate for the solution of the initial value problem for the heat equation governed by L in terms of the Lp norm of the initial data for 1 ≤ p ≤ ∞. This research has been partially supported by...