Related papers: On the Spectral Large Sieve Inequality for $\mathr…
We apply power series expansion to symmetric multi-well oscillators bounded by two infinite walls. The spectrum and expectation values obtained are compared with available exact and approximate values for the unbounded ones. It is shown…
The Whittle likelihood is a widely used and computationally efficient pseudo-likelihood. However, it is known to produce biased parameter estimates for large classes of models. We propose a method for de-biasing Whittle estimates for…
In this paper, we develop a large sieve type inequality for some special characters whose moduli are squares of primes. Our result gives non-trivial estimate in certain ranges.
Spectral enhancement -- which aims to undo spectral broadening -- leads to integral equations which are ill-posed and require special regularisation techniques for their solution. Even when an optimal regularisation technique is used,…
We obtain a sharp estimate for the best constant $C>0$ in the Wirtinger type inequality \[ \int_0^{2\pi}\gamma^pw^2\le C\int_0^{2\pi}\gamma^qw'^2 \] where $\gamma$ is bounded above and below away from zero, $w$ is $2\pi$-periodic and such…
In this work we prove analogues of Bessel inequality and Riesz-Fisher theorem in Hilbert spaces with respect to sequences. We apply our generalized Bessel inequality to the Hilbert spaces associated with the Normal, Beta, Gamma and certain…
In this note we give a new bound for large sieve with characters to power moduli which improves in some range of the parameters the previous bounds of Baier/Zhao and Halupczok.
We give a new bound for the large sieve inequality with power moduli q^k that is uniform in k. The proof uses a new theorem due to T. Wooley from his work on efficient congruencing.
We establish large sieve inequalities for power moduli in imaginary quadratic number fields, extending earlier work of Baier and Bansal for the Gaussian field.
Let $L$ be a non-negative self adjoint operator acting on $L^2(X)$ where $X$ is a space of homogeneous type. Assume that $L$ generates a holomorphic semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ have Gaussian upper bounds but possess no…
Laser speckle, the granular intensity pattern arising from random optical interference, provides a high-dimensional encoding of spectral information that can be exploited for precision metrology. Speckle-based spectrometers have advanced…
In this paper, we provide suitable characterisations of pairs of weights $(V,W),$ known as Bessel pairs, that ensure the validity of weighted Hardy-type inequalities. The abstract approach adopted here makes it possible to establish such…
Welch's method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite length time series,…
We first interpret Pell's equation satisfied by Chebyshev polynomials for each degree t, as a certain Positivstellensatz, which then yields for each integer t, what we call a generalized Pell's equation, satisfied by reciprocals of…
In this article, we establish a large sieve inequality for additive characters to moduli in the range of appropriate integer polynomials of degree two. As an application, we derive a weighted zero-density estimate for twists of…
We obtain spectral estimates for the iterations of Ruelle operator $L_{f + (a + \i b)\tau + (c + \i d) g}$ with two complex parameters and H\"{o}lder functions $f,\: g$ generalizing the case $\Pr(f) =0$ studied in [PeS2]. As an application…
We obtain new inequalities for the modified Bessel function of the second kind $K_\nu$ in terms of the gamma function. These bounds follow as special cases of inequalities that we derive for the kernel of the Kr\"{a}tzel integral…
The transmutation (transformation) operator associated with the perturbed Bessel equation is considered. It is shown that its integral kernel can be uniformly approximated by linear combinations of constructed here generalized wave…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of…