Weakly invertible elements in anisotropic weighted spaces of holomorphic functions in a polydisc

Abstract

In this paper we investigate trans-impedance amplifiers which can be used to minimize the influence of stray capacitances on the operation of signal conditioners used for instrumentation applications such as inductive microsensors for micromachines. The effect of stray capacitances can be minimized when using this type of amplifier by ensuring that its input impedance is small. A technique for realizing very low input impedances over a wide bandwidth for these amplifiers is studied both analytically and experimentally for transistors having a wide range of gain-bandwidth products f T . In addition an improved circuit configuration which further reduces the amplifier's input impedance at high frequencies is investigated by computer simulation.

In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc

“…Also, the author is aware of the existence of a huge litterature on the function theory in polydiscs and other domains in C n , but he found almost no information on cyclic functions. We quote however several papers on polydisc invariant subspace theory, [1], [10], [20], [25], [26], [12], [24], [28]. A few of more specific comments as well as historical remarks are collected below.…”

On a class of inner functions in a half-space

“…We note that the conditions ∈ ∞ (︀ C + )︀ and ( ) ̸ = 0, ∈ C + , are not sufficient for the weak invertibility of function in space (︀ C + )︀ . Indeed, in view of the results of work [8], it is easy to establish that the functions…”

A weak invertibility criterion in the weighted L p -spaces of holomorphic functions in the ball

“…The next statement for 1 ≤ p < +∞ in the case of the unit ball was established in [6,7] and in the case of the polydisk, in [12].…”

“…In the one-dimensional case the study begun by Keldysh [4] of weakly invertible elements was continued by many authors (see [5][6][7][8][9][10][11]). In the multidimensional case in the weighted anisotropic spaces of holomorphic functions in the polydisk the author studied [12,13] the weak invertibility of bounded analytic functions.…”