Search results for "Multiplier"

A note on the Schur multiplier of a nilpotent Lie algebra

2011

For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong H(1)\oplus A$, where $A$ is an abelian Lie algebra of dimension $n-3$ and H(1) is the Heisenberg algebra of dimension 3.

On the Minimal Solution of the Problem of Primitives

2000

Abstract We characterize the primitives of the minimal extension of the Lebesgue integral which also integrates the derivatives of differentiable functions (called the C -integral). Then we prove that each BV function is a multiplier for the C -integral and that the product of a derivative and a BV function is a derivative modulo a Lebesgue integrable function having arbitrarily small L 1 -norm.

On some dual frames multipliers with at most countable spectra

2021

A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames in a Hilbert space, respectively. In this paper we investigate the spectra of some dual frames multipliers giving, in particular, conditions to be at most countable. The contribution extends the results available in literature about the spectra of Bessel multipliers with symbol decaying to zero and of multipliers of dual Riesz bases.

Some considerations on the nonabelian tensor square of crystallographic groups

2011

The nonabelian tensor square $G\otimes G$ of a polycyclic group $G$ is a polycyclic group and its structure arouses interest in many contexts. The same assertion is still true for wider classes of solvable groups. This motivated us to work on two levels in the present paper: on a hand, we investigate the growth of the Hirsch length of $G\otimes G$ by looking at that of $G$, on another hand, we study the nonabelian tensor product of pro--$p$--groups of finite coclass, which are a remarkable class of solvable groups without center, and then we do considerations on their Hirsch length. Among other results, restrictions on the Schur multiplier will be discussed.

On the presence of families of pseudo-bosons in nilpotent Lie algebras of arbitrary corank

2019

We have recently shown that pseudo-bosonic operators realize concrete examples of finite dimensional nilpotent Lie algebras over the complex field. It has been the first time that such operators were analyzed in terms of nilpotent Lie algebras (under prescribed conditions of physical character). On the other hand, the general classification of a finite dimensional nilpotent Lie algebra $\mathfrak{l}$ may be given via the size of its Schur multiplier involving the so-called corank $t(\mathfrak{l})$ of $\mathfrak{l}$. We represent $\mathfrak{l}$ by pseudo-bosonic ladder operators for $t(\mathfrak{l}) \le 6$ and this allows us to represent $\mathfrak{l}$ when its dimension is $\le 5$.

Representations of Finite Groups

2009

Multipliers on Vector Valued Bergman Spaces

2002

AbstractLet X be a complex Banach space and let Bp(X) denote the vector-valued Bergman space on the unit disc for 1 ≤ p < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y defines a multiplier between Bp(X) and Bq(Y) (resp. Bp(X) and lq(Y)) if for any function we have that belongs to Bq(Y) (resp. (Tn(xn))n ∈ lq(Y)). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces X and Y. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in Bp(X) are introduced.

A description of pseudo-bosons in terms of nilpotent Lie algebras

2017

We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic-geometric structure of this kind is observed in the context of pseudo-bosonic operators. Indeed we don't find the well known Heisenberg algebras, which are involved in several quantum dynamical systems, but different Lie algebras which may be decomposed in the sum of two abelian Lie algebras in a prescribed way. We introduce the notion of semidirect sum (of Lie algebras) for this scope and find that it describes very well the behaviour of pseudo-bosonic operators in many quantum models.

Modeling and Characterization of SiPM Parameters at Temperatures between 95 K and 300 K

2017

The modeling and characterization of silicon photomultipliers (SiPMs) in a wide temperature range from 95 K to 300 K is presented. The devices under study had the distinctive feature of forward-biased p-n junctions situated under each pixel as active quenching resistors making them particularly appropriate to be operated at cryogenic temperatures. The voltage drop across the diode in a forward direction was measured for a series of injected currents in this temperature range. It was observed that the characteristics of different SiPM types influence the temperature dependence of the reverse saturation current. The devices were further characterized by low-level light-pulse measurements. The…

On the operation of silicon photomultipliers at temperatures of 1–4 kelvin

2016

Abstract SiPM operation at cryogenic temperatures fails for many common devices. A particular type from Zecotek with deep channels in the silicon substrate instead of quenching resistors was tested at liquid helium temperature. Two similar types were thoroughly characterized from room temperature down to liquid nitrogen temperature by illuminating them with low light levels. At cryogenic temperatures the SiPMs show an unchanged rise-time and a fast recovery time, practically no after-pulses, and exhibit no increased cross-talk probability. Charge collection spectra were measured to extract the pixel gain and its variation, both comparable to room temperature at the same over-voltage. The qu…