We prove that a bounded stack can be specified in process algebra with just the operators alternative and sequential composition and iteration. The bounded bag cannot be specified with these operators, but can be specified if we add the parallel composition operator without communication (free merge). The bounded queue cannot even be specified in this signature; we need a form of variable bindi...

We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the l∞-norm, that is, by a...

Let X be a Banach space and T be a bounded linear operator from X to itself (T ∈ B(X)). An operator S ∈ B(X) is a generalised inverse of T if TST = T . In this paper we look at the Jörgens algebra, an algebra of operators on a dual system, and characterise when an operator in that algebra has a generalised inverse that is also in the algebra. This result is then applied to bounded inner product...

We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain $\Omega$ subject to homogeneous Dirichlet boundary conditions. prove $\mathrm{L}^p$-resolvent estimates for $p$ satisfying condition $\lvert 1 / p - 2 \rvert < 4 + \varepsilon$ some $\varepsilon > 0$. further show that operator admits property of maximal regularity and its $\mathrm{H}^{\infty}$-calculus is bo...

DAEs: Infinite-dimensional LTI Index-1 Case 3.1 Infinite-dimensional Linear Algebra We first collect some useful infinite-dimensional definitions and statements which will be used in this and the next section. Details and proofs of these statements can be found in standard functional analysis references such as [11], [26], [28] and [38]: Proposition 3.1. Let L(X,Y ) denote the space of bounded ...

Let 1 < p ≤ q < +∞ and let v, w be weights on (0,+∞) satisfying: (?) v(x)xis equivalent to a non-decreasing function on (0,+∞) for some ρ ≥ 0; [w(x)x] ≈ [v(x)x] for all x ∈ (0,+∞). We prove that if the averaging operator (Af)(x) := 1 x R x 0 f(t) dt, x ∈ (0,+∞), is bounded from the weighted Lebesgue space Lp((0,+∞); v) into the weighted Lebesgue space Lq((0,+∞);w), then there exists ε0 ∈ (0, p−...