Related papers: Random Menshov spectra
In this paper, we consider representations of integers as sums of generalized heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such…
Line-narrowing by periodic modulation of nuclear spin interaction Hamiltonians is the central element of various experimental techniques in NMR spectroscopy. In this study, we present a theoretical formulation of coherent averaging to…
Given N quantum systems prepared according to the same density operator \rho, we propose a measurement on the N-fold system which approximately yields the spectrum of \rho. The projections of the proposed observable decompose the Hilbert…
In this paper, we study the spectrality of infinite convolutions generated by infinitely many admissible pairs which may not be compactly supported, where the spectrality means the corresponding square integrable function space admits a…
We revisit the concept of spectral averaging and point out its origin in connection with one-parameter subgroups of $SL_2(\bbR)$ and the corresponding M\"obius transformations. In particular, we identify exponential Herglotz representations…
We prove that univalent harmonic mappings can be approximated by univalent Fourier series of step functions.
We demonstrate that an effect other than anharmonicity can severely distort the spectroscopic signatures of quantum mechanical systems. This is done through an analytic calculation of the spectroscopic response of a simple system, a charged…
This paper is concerned with the Lyapunov spectrum for measurable cocycles over an ergodic pmp system taking values in semi-simple real Lie groups. We prove simplicity of the Lyapunov spectrum and its continuity under certain perturbations…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
Whenever we have a group acting on a class of functions by translation, the bispectrum offers a principled and lossless way of representing such functions invariant to the action. Unfortunately, computing the bispectrum is often costly and…
By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix…
Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
We provide generating functions for the perturbative massive string spectrum which are covariant with respect to the SO(9) little group, and which contain all the representation theoretic content of the spectrum. Generating functions for…
By the theory of elliptic curves, we study the integers representable as the product of the sum of four integers with the sum of their reciprocals and give a sufficient condition for the integers with a positive representation.
It is now well understood that convex programming can be used to estimate the frequency components of a spectrally sparse signal from $2m+1$ uniform temporal measurements. It is conjectured that a phase transition on the success of the…
We study the random sampling of band-limited functions of several variables. If a bandlimited function with bandwidth one has its essential support on a cube of volume $R^d$, then $\cO (R^d \log R^d)$ random samples suffice to approximate…
Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial…
The problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions. The first one describes the wave scattered by the random…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…