作者：
Chavez, AlanHuatangari, Lenin QuinonesUniv Nacl Trujillo
Inst Invest Matemat OASIS Res Grp FCFYM Ave Juan Pablo 2S-N-Urbanizac San Andres Trujillo 13011 Peru Univ Nacl Trujillo
Inst Invest Matemat GRACOCC Res Grp FCFYM Ave Juan Pablo 2S-N-Urbanizac San Andres Trujillo 13011 Peru Univ Nacl Trujillo
Dept Matemat FCFYM Ave Juan Pablo 2S-N-Urbanizac San Andres Trujillo 13011 Peru Univ Nacl Jaen
Inst Ciencia Datos Cajamarca Peru
In the present work, for X a Banach space, the notion of piecewise continuous Zalmost automorphic functions with values in finite dimensional spaces is extended to piecewise continuous Z-almost automorphic functions w...
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In the present work, for X a Banach space, the notion of piecewise continuous Zalmost automorphic functions with values in finite dimensional spaces is extended to piecewise continuous Z-almost automorphic functions with values in X. Several properties of this class of functions are provided, in particular it is shown that if Xis a Banach algebra, then this class of functions constitute also a Banach algebra;furthermore, using the theory of Z-almost automorphic functions, a new characterization of compact almost automorphic functions is given. As consequences, with the help of Z-almost automorphic functions, it is presented a simple proof of the characterization of almost automorphic sequences by compact almost automorphic functions;the method permits us to give explicit examples of compact almost automorphic functions which are not almost periodic. Also, using the theory developed here, it is shown that almost automorphic solutions of differential equations with piecewise constant argument are in fact compact almost automorphic. Finally, it is proved that the classical solution of the 1D D heat equation with continuous Z-almost automorphic source is also continuous Z-almost automorphic;furthermore, we comment applications to the existence and uniqueness of the asymptotically continuous Z-almost automorphic mild solution to abstract integro-differential equations with nonlocal initial conditions. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
We provide a concrete characterization of the poly-analytic planar automorphic functions, a special class of non analytic planar automorphic functions with respect to the Appell-Humbert automorphy factor, arising as i...
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We provide a concrete characterization of the poly-analytic planar automorphic functions, a special class of non analytic planar automorphic functions with respect to the Appell-Humbert automorphy factor, arising as images of the holomorphic ones by means of the creation differential operator. This is closely connected to the spectral theory of the magnetic Laplacian on the complex plane.
The construction of analogues of the Cauchy kernel is crucial for the solution of Riemann-Hilbert problems on compact Riemann surfaces. A formula for the Cauchy kernel can be given as an infinite sum over the elements...
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The construction of analogues of the Cauchy kernel is crucial for the solution of Riemann-Hilbert problems on compact Riemann surfaces. A formula for the Cauchy kernel can be given as an infinite sum over the elements of a Schottky group, and this sum is often used for the explicit evaluation of the kernel. In this paper a new formula for a quasi-automorphic analogue of the Cauchy kernel in terms of the Schottky-Klein prime function of the associated Schottky double is derived. This formula opens the door to finding new ways to evaluate the analogue of the Cauchy kernel in cases where the infinite sum over a Schottky group is not absolutely convergent. Application of this result to the solution of the Riemann-Hilbert problem with a discontinuous coefficient for symmetric automorphic functions is discussed.
We investigate the spectral theory of the invariant Landau Hamiltonian, L-nu = -1/2{4 Sigma(n)(j=1)partial derivative(2)/partial derivative z(j)partial derivative(z) over bar (j) + 2 nu Sigma(n)(j=1)(z(j)partial deriv...
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We investigate the spectral theory of the invariant Landau Hamiltonian, L-nu = -1/2{4 Sigma(n)(j=1)partial derivative(2)/partial derivative z(j)partial derivative(z) over bar (j) + 2 nu Sigma(n)(j=1)(z(j)partial derivative/partial derivative z(j)-(z) over bar (j)partial derivative/partial derivative(z) over bar (j))-nu(2)vertical bar z vertical bar(2)}, acting on the space F-Gamma,chi(nu) of (Gamma,chi)-automorphic functions on C-n, constituted of C-infinity functions satisfying the functional equation f(z+gamma) = chi(gamma)e(i nu Jm < z,gamma >)f(z);z is an element of C-n, gamma is an element of Gamma, for given real number nu > 0, lattice Gamma of C-n and a map chi:Gamma-->U(1) such that the triplet (nu,Gamma,chi) satisfies a Riemann-Dirac quantization-type condition. More precisely, we show that the eigenspace epsilon(nu)(Gamma,chi)(lambda) = {f is an element of F-Gamma,chi(nu);L(nu)f=nu(2 lambda+nf};lambda is an element of C, is nontrivial if and only if lambda=l=0,1,2,...,. In such case, epsilon(nu)(Gamma,chi)(l) is a finite dimensional vector space whose the dimension is given explicitly by [GRAPHICS] Furthermore, we show that the eigenspace epsilon(nu)(Gamma,chi)(0) associated with the lowest Landau level of L-nu is isomorphic to the space, O-Gamma,chi(nu)(C-n), of holomorphic functions on C-n satisfying g(z+gamma)=chi(gamma)e(nu/2 vertical bar gamma vertical bar 2+nu < z,gamma >)g(z), (*) that we can realize also as the null space of the differential operator, Sigma(n)(j=1)(-partial derivative(2)/partial derivative z(j)partial derivative(z) over bar (j) + nu(z) over bar (j)partial derivative/partial derivative(z) over bar (j)) acting on C-infinity functions of C-n satisfying (*). (C) 2008 American Institute of Physics.
For a given discrete subgroup Gamma of (C,+) and given real number nu>0, we study the spectral properties of the magnetic Laplacian operator Delta(nu) acting on the Hilbert space L-Gamma,chi(2,nu) (C) of (L-2,Gamma...
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For a given discrete subgroup Gamma of (C,+) and given real number nu>0, we study the spectral properties of the magnetic Laplacian operator Delta(nu) acting on the Hilbert space L-Gamma,chi(2,nu) (C) of (L-2,Gamma)-automorphic functions (see below for notations). We show that its spectrum is reduced to the eigenvalues nu m;m = 0,1,.... We also give a concrete description of each eigenspace in terms of the Hermite polynomials. This description will be used to characterize the range of true Bargmann transform of L-2-periodic functions on the real line R. Published by AIP Publishing.
The purpose of this paper is to develop a scattering theory for twisted automorphic functions on the hyperbolic plane, defined by a cofinite (but not cocompact) discrete group Gamma with an irreducible unitary represe...
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The purpose of this paper is to develop a scattering theory for twisted automorphic functions on the hyperbolic plane, defined by a cofinite (but not cocompact) discrete group Gamma with an irreducible unitary representation rho and satisfying u(gamma z) = rho(gamma)u(z). The Lax-Phillips approach is used with the wave equation playing a central role. Incoming and outgoing subspaces are employed to obtain corresponding unitary translation representations, R- and R+, for the solution operator. The scattering operator, which maps R(-)f into R(+)f, is unitary and commutes with translation. The spectral representation of the scattering operator is a multiplicative operator, which can be expressed in terms of the constant term of the Eisenstein Series. When the dimension of rho is one, the elements of the scattering operator cannot vanish. However when dim(rho) > 1 this is no longer the case.
We first propose two types of concepts of almost automorphic functions on the quantum time scale. Secondly, we study some basic properties of almost automorphic functions on the quantum time scale. Then, we introduce ...
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We first propose two types of concepts of almost automorphic functions on the quantum time scale. Secondly, we study some basic properties of almost automorphic functions on the quantum time scale. Then, we introduce a transformation between functions defined on the quantum time scale and functions defined on the set of generalized integer numbers;by using this transformation we give equivalent definitions of almost automorphic functions on the quantum time scale;following the idea of the transformation, we also give a concept of almost automorphic functions on more general time scales that can unify the concepts of almost automorphic functions on almost periodic time scales and on the quantum time scale. Finally, as an application of our results, we establish the existence of almost automorphic solutions of linear and semilinear dynamic equations on the quantum time scale.
In this paper, we first formulate the Well explicit formula of prime number theory for cuspidal automorphic L-functions L(s, pi) of GL(d). Then, we prove some conditional results about the vanishing order at the centr...
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In this paper, we first formulate the Well explicit formula of prime number theory for cuspidal automorphic L-functions L(s, pi) of GL(d). Then, we prove some conditional results about the vanishing order at the central point of L(s, pi). This enables to yield an estimate for the height of the lowest zero of L(s, pi) on the critical line in terms of the analytic conductor. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
This paper is the first in a series of two dedicated to the study of period relations of the type L (1/2 + k, Pi) is an element of (2 pi i)(d.k)Omega(k)((-1)) Q(Pi), 1/2 + k critical, for certain automorphic represent...
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This paper is the first in a series of two dedicated to the study of period relations of the type L (1/2 + k, Pi) is an element of (2 pi i)(d.k)Omega(k)((-1)) Q(Pi), 1/2 + k critical, for certain automorphic representations. of a reductive group G. In this paper we discuss the case G = GL(n+1) x GL(n). The case G = GL(2n) is discussed in part two. Our method is representation theoretic and relies on the author's recent results on global rational structures on automorphic representations. We show that the above period relations are intimately related to the field of definition of the global representation. under consideration. The new period relations we prove are in accordance with Deligne's Conjecture on special values of L-functions, and the author expects this method to apply to other cases as well.
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