TY  - JOUR
AB  - We are looking at families of functions or measures on the torus which are specified by a finite number of parameters N. The task, for a given family, is to look at a small number of Fourier coefficients of the object, at a set of locations that is predetermined and may depend only on N, and determine the object. We look at (a) the indicator functions of at most N intervals of the torus and (b) at sums of at most N complex point masses on the multidimensional torus. In the first case we reprove a theorem of Courtney which says that the Fourier coefficients at the locations 0 , 1 , … , N are sufficient to determine the function (the intervals). In the second case we produce a set of locations of size O(Nlog d-1N) which suffices to determine the measure.
AU  - Diederichs, B.
AU  - Kolountzakis, M.N.*
AU  - Papageorgiou, E.*
C1  - 66530
C2  - 53203
SP  - 23–42
TI  - How many Fourier coefficients are needed?
JO  - Monatsh. Math.
VL  - 200
PY  - 2023
SN  - 0026-9255
ER  - 

TY  - JOUR
AB  - We establish the solvability of certain linear nonhomogeneous equations and demonstrate that under reasonable technical conditions the convergence in L2(Rd) of their right sides implies the existence and the convergence in L2(Rd) of the solutions. In the first part of the work the equation involves the logarithmic Laplacian. In the second part we generalize the results derived by incorporating a shallow, short-range scalar potential into the problem. The argument relies on the methods of the spectral and scattering theory for the non-Fredholm Schrödinger type operators. As distinct from the preceding articles on the subject, for the operators involved in the equations the essential spectra fill the whole real line.
AU  - Efendiyev, M.A.
AU  - Vougalter, V.*
C1  - 68165
C2  - 53610
CY  - Prinz-eugen-strasse 8-10, A-1040 Vienna, Austria
SP  - 751–771
TI  - Solvability in the sense of sequences for some non-Fredholm operators with the logarithmic Laplacian.
JO  - Monatsh. Math.
VL  - 202
IS  - 4
PB  - Springer Wien
PY  - 2023
SN  - 0026-9255
ER  - 

TY  - JOUR
AB  - We study modifications of Reiter’s condition (Pr ) which are generated bycertain power and root procedures. In thatwaywe can illustrate the difference between the (P1)- and the (P2)-property. Furthermore we present equivalent conditions to (P2). In order to have examples we discuss the results for polynomial hypergroups.
AU  - Lasser, R.
AU  - Skantharajah, M.
C1  - 4734
C2  - 28533
SP  - 327-338
TI  - Reiter's condition for amenable hypergroups.
JO  - Monatsh. Math.
VL  - 163
IS  - 3
PB  - Springer
PY  - 2011
SN  - 0026-9255
ER  - 

TY  - JOUR
AB  - Let K be a commutative hypergroup with the Haar measure 
. In the present paper we investigate whether the maximal ideals in L1ðK; 
Þ have bounded approximate identities. We will show that the existence of a bounded approximate identity is equivalent to the existence of certain functionals on the space L1ðK; 
Þ. Finally we apply the results to polynomial hypergroups and obtain a rather complete solution for this class.
AU  - Filbir, F.
AU  - Lasser, R.
AU  - Szwarc, R.*
C1  - 22786
C2  - 31068
SP  - 189-203
TI  - Reiter’s condition P1 and approximate identities for polynomial hypergroups.
JO  - Monatsh. Math.
VL  - 143
IS  - 3
PB  - Springer
PY  - 2004
SN  - 0026-9255
ER  - 

TY  - JOUR
AB  - The one-step prediction problem is studied in the context of Pn-weakly stationary stochastic processes {Mathematical expression}, where {Mathematical expression} is an orthogonal polynomial sequence defining a polynomial hypergroup on {Mathematical expression}. This kind of stochastic processes appears when estimating the mean of classical weakly stationary processes. In particular, it is investigated whether these processes are asymptotic Pn-deterministic, i.e. the prediction mean-squared error tends to zero. Sufficient conditions on the covariance function or the spectral measure are given for {Mathematical expression} being asymptotic Pn-deterministic. For Jacobi polynomials Pn(x) the problem of {Mathematical expression} being asymptotic Pn-deterministic is completely solved.
AU  - Hösel, V.
AU  - Lasser, R.H.
C1  - 40629
C2  - 38015
SP  - 199-212
TI  - One-step prediction for Pn-weakly stationary processes.
JO  - Monatsh. Math.
VL  - 113
IS  - 3
PY  - 1992
SN  - 0026-9255
ER  - 

TY  - JOUR
AB  - Consider the Laguerre functionslpn(t)=(−1)n2p−−√Ln(2pt)e−pt (with parameterp>0), where theL  n  are the Laguerre polynomials with parameter α=0.{l   n   p  (t)}  n=0  ∞  forms a complete orthonormal system inL 2 ([0, ∞)). A well known and often used property of the Laguerre functions is the convolution property:2p−−√lpi∗lpj=lpi+j+lpi+j+1 for alli,j≥0. It is the objectiveof this note that the system of Laguerre functions is the only complete and orthonormal system ofL 2 ([0, ∞)) satisfying the convolution property.
AU  - Budke, G.
C1  - 17652
C2  - 10563
SP  - 281-285
TI  - On a Convolution Property Characterizing the Laguerre Functions.
JO  - Monatsh. Math.
VL  - 107
PY  - 1989
SN  - 0026-9255
ER  -