Let G be a locally compact group. Then G is known to be amenable if and only if it has Reiter’s property (P1), i.e., there is a net (mα)α of non-negative norm one functions in L(G) such that limα supx∈K ‖Lx−1mα−mα‖ = 0 for each compact subset K ⊂ G (Lx−1mα stands for the left translate of mα by x). We give a formulation of property (P1) that extends naturally to locally compact quantum groups i...

In this paper two R‑L network simulator configurations employing a single VDDIBA, one resistance and one grounded capacitance are presented. The first configuration is a grounded series resistor-inductor (R‑L) network simulator and the second configuration is intended for grounded parallel resister-inductor (R‑L) circuit simulation. Both the proposed circuits enjoy several beneficial features s...

Consider a locally compact groupG and consider some appropriate group algebras. The group algebras C[G] for G as an abstract group is not enough to define the structure of G. We must find a more effective group algebra. For any locally compact group G there is a natural left-(right-)invariant Haar measure dg. The space L(G) := L(G, dg) of the square-integrable functions plays an important role ...

Let G be a locally compact group. Then G is known to be amenable if and only if it has Reiter’s property (P1), i.e., there is a net (mα)α of non-negative norm one functions in L(G) such that limα supx∈K ‖Lx−1mα−mα‖ = 0 for each compact subset K ⊂ G (Lx−1mα stands for the left translate of mα by x). We give a formulation of property (P1) that extends naturally to locally compact quantum groups i...

We study the structure of strictly singular non-compact operators between $L\_p$ spaces. Answering a question raised in earlier work on interpolation properties operators, it is shown that there exist $T$, for which set points $(1/p,1/q)\in(0,1)\times (0,1)$ such $T\colon L\_p\rightarrow L\_q$ but not compact contains line segment triangle ${(1/p,1/q):1\<p\<q<\infty}$ any positive slope. This w...

Let G be a locally compact group, 1 < p < ∞ and let ω be a weight function on G. Recently, we introduced the Lebesgue weighted L−algebra L ω (G). Here, we establish necessary and sufficient conditions for L ω (G) to be φ−contractible, pseudo-contractible or contractible. Moreover we give some similar results about L(G,ω).

We consider global solvability of complex vector fields on noncompact manifolds. The case of real vector fields had been considered by Malgrange, and Hörmander studied the complex case, assuming that the real and imaginary parts are everywhere linearly independent. 1. We consider a smooth complex vector field L = X + iY without zeros on a smooth, paracompact, noncompact manifold M. The real vec...

(Preface page 4 L. -13) Yorke (1990) should be Nusse and Yorke (1990). p. 4 (L. -2) Subsections 8.3.1 – 4 p. 10 (L. -3) “could be combined with the section in Chapter VIII).” p. 17 (L. 2) {(x, f(x)} should read {(x, f(x))}. p. 24 (L. -12) should be “compact nested nonempty sets.” p. 24 (L. -4) should be “ . . . is closed and positively invariant . . . ” p. 27 (L. 3) “A non-empty set S . . . ” p...

For n ≥ 2 a construction is given for convex bodies K and L in R n such that the orthogonal projection Ku can be translated inside Lu for every direction u, while the volumes of K and L satisfy Vn(K) > Vn(L). A more general construction is then given for n-dimensional convex bodies K and L such that the orthogonal projection Kξ can be translated inside Lξ for every k-dimensional subspace ξ of R...