Related papers: An operator theoretic approach to the Prime number…

We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an absolutely integrable function and a trace class operator, or of two trace class operators. Our results include…

In this note we examine Littlewood's proof of the prime number theorem. We show that this can be extended to provide an equivalence between the prime number theorem and the non-vanishing of Riemann's zeta-function on the one-line. Our…

We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.

We consider the classical Wiener-Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known…

By using the elementary symmetric polynomials and some results of number theory, we solve the well known problem of Lehmer on Euler's totient function. As application, we obtain a new characterization of prime numbers.

We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem…

In this paper, a new generalized Bernstein-Bezier type operators is constructed.The estimates of the moments of these operators are investigated. The rate of convergence in terms of modulus of continuity is given. Then, the equivalent…

In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.

In this pedagogical note I present the operator form of Wick's theorem, i.e. a procedure to bring a product of 1-particle creation and destruction operators to normal order, with respect to some reference many-body state. Both the static…

We prove a genuine analogue of Wiener Tauberian theorem for hypergeometric transforms. As an application we prove analogue of Furstenberg theorem on Harmonic functions.

By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. The usefulness of the…

In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

We give a short direct proof of Agler's factorization theorem that uses the abstract characterization of operator algebras. the key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional…

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.

A Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theorems appear in a tremendous variety of applications, ranging…

The prime number theorem provided the chief impulse for complex Tauberian theory, in which the boundary behavior of a transform in the complex plane plays a crucial role. We consider Laplace transforms of bounded functions. Our Tauberian…

With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for…

By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichl\'et problems for planar Jordan domains with at least two boundary curves. An iterative method is thus obtained,…

A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…