Publications (30)
A new method to generate superoscillating functions and supershifts
Y. Aharonov, F. Colombo, I. Sabadini +3
Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechani…
A new functional calculus for non-commuting operators
F. Colombo, I. Sabadini, D. C. Struppa
In this paper we use the notion of slice monogenic functions \cite{slicecss} to define a new functional calculus for an -tuple of not necessarily commuting operators. This c…
A unified approach to the Dirac fine structures on the -spectrum and a connection with Jacobi polynomials
F. Colombo, A. De Martino, S. Pinton
This paper contributes to the recently introduced theory of fine structures on the -spectrum. We study, in a unified way, the functional calculi for axially Poly-Analytic-Harmon…
Positive and generalized positive real lemma for slice hyperholomorphic functions
D. Alpay, F. Colombo, I. Lewkowicz +1
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic function…
Superoscillations in the hypercomplex setting
F. Colombo, F. Mantovani, S. Pinton +1
Superoscillatory functions represent a counterintuitive phenomenon in physics but also in mathematics, where a band-limited function oscillates faster than its highest Fourier comp…
Analyticity, superoscillations and supershifts in several variables
F. Colombo, I. Sabadini, D. C. Struppa +1
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon pe…
Test Beam Performance Measurements for the Phase I Upgrade of the CMS Pixel Detector
M. Dragicevic, M. Friedl, J. Hrubec +481
A new pixel detector for the CMS experiment was built in order to cope with the instantaneous luminosities anticipated for the Phase~I Upgrade of the LHC. The new CMS pixel detecto…
Non commutative functional calculus: unbounded operators
F. Colombo, G. Gentili, I. Sabadini +1
In a recent work, \cite{cgss}, we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from \cite{cgss…
Slice monogenic functions
F. Colombo, I. Sabadini, D. C. Struppa
In this paper we offer a definition of monogenicity for functions defined on $\rr^{n+1}$ with values in the Clifford algebra $\rr_n$ following an idea inspired by the recent papers…
The mathematics of superoscillations
Y. Aharonov, F. Colombo, I. Sabadini +2
In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed t…
Boundary interpolation for slice hyperholomorphic Schur functions
K. Abu-Ghanem, D. Alpay, F. Colombo +2
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers , quaternions $p_1, \ldots, p_N…
Trapping in irradiated p-on-n silicon sensors at fluences anticipated at the HL-LHC outer tracker
W. Adam, T. Bergauer, M. Dragicevic +682
The degradation of signal in silicon sensors is studied under conditions expected at the CERN High-Luminosity LHC. 200 m thick n-type silicon sensors are irradiated with proton…
Entire monogenic functions of given proximate order and continuous homomorphisms
F. Colombo, R. S. Krausshar, S. Pinton +1
Infinite order differential operators appear in different fields of mathematics and physics. In the past decade they turned out to play a crucial role in the theory of superoscilla…
The spectral theorem for unitary operators based on the -spectrum
D. Alpay, F. Colombo, D. P. Kimsey +1
The quaternionic spectral theorem has already been considered in the literature, see e.g. [22], [31], [32], however, except for the finite dimensional case in which the notion of s…
Analyticity and supershift with regular sampling
F. Colombo, I. Sabadini, D. C. Struppa +1
The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interv…
Planck pre-launch status: calibration of the Low Frequency Instrument flight model radiometers
F. Villa, L. Terenzi, M. Sandri +71
The Low Frequency Instrument (LFI) on-board the ESA Planck satellite carries eleven radiometer subsystems, called Radiometer Chain Assemblies (RCAs), each composed of a pair of pse…
Analyticity and supershift with irregular sampling
F. Colombo, I. Sabadini, D. C. Struppa +1
The notion of supershift generalizes that one of superoscillation and expresses the fact that the sampling of a function in an interval allows to compute the values of the function…
Bloch, Besov and Dirichlet spaces of slice hyperholomorphic functions
C. M. P. Castillo Villalba, F. Colombo, J. Gantner +1
In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the…
Dynamic validation of the Planck/LFI thermal model
M. Tomasi, B. Cappellini, A. Gregorio +12
The Low Frequency Instrument (LFI) is an array of cryogenically cooled radiometers on board the Planck satellite, designed to measure the temperature and polarization anisotropies…
Adaptive orthonormal systems for matrix-valued functions
D. Alpay, F. Colombo, T. Qian +1
In this paper we consider functions in the Hardy space defined in the unit disc of matrix-valued. We show that it is possible, as in the scalar case, to…
The functional calculus based on the -spectrum for quaternionic operators and for -tuples of noncommuting operators
D. Alpay, F. Colombo, T. Qian +1
In this paper we extend the functional calculus to quaternionic operators and to -tuples of noncommuting operators using the theory of slice hyperholomorphic function…
Planck pre-launch status: Low Frequency Instrument calibration and expected scientific performance
A. Mennella, M. Bersanelli, R. C. Butler +83
We give the calibration and scientific performance parameters of the Planck Low Frequency Instrument (LFI) measured during the ground cryogenic test campaign. These parameters char…
The S-functional calculus for the Clifford adjoint operator
F. Colombo, F. Mantovani, P. Schlosser
In this paper, we work within the framework of modules over the Clifford algebra . Our investigation focuses on the S-spectrum and the S-functional calculus in its va…
An extension of Herglotz's theorem to the quaternions
D. Alpay, F. Colombo, D. P. Kimsey +1
A classical theorem of Herglotz states that a function from into is positive definite if and only there exists a $\mathbb C^{s\t…
Beurling-Lax type theorems and Cuntz relations
D. Alpay, F. Colombo, I. Sabadini +1
We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also stu…
The quantum pigeonhole principle and the nature of quantum correlations
Y. Aharonov, F. Colombo, S. Popescu +3
The pigeonhole principle: "If you put three pigeons in two pigeonholes at least two of the pigeons end up in the same hole" is an obvious yet fundamental principle of Nature as it…
Quantum harmonic oscillator with superoscillating initial datum
R. V. Buniy, F. Colombo, I. Sabadini +1
In this paper we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the…
Planck pre-launch status: Design and description of the Low Frequency Instrument
M. Bersanelli, N. Mandolesi, R. C. Butler +109
In this paper we present the Low Frequency Instrument (LFI), designed and developed as part of the Planck space mission, the ESA program dedicated to precision imaging of the cosmi…
Non commutative functional calculus: bounded operators
F. Colombo, G. Gentili, I. Sabadini +1
In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the notion of slice-regularity, see \cite{gs},…
Gauss sums, superoscillations and the Talbot carpet
F. Colombo, I. Sabadini, D. C. Struppa +1
We consider the evolution, for a time-dependent Schrödinger equation, of the so called Dirac comb. We show how this evolution allows us to recover explicitly (indeed optically) th…