The theory of Liouville functions
نویسنده
چکیده
A Liouville function is an analytic function H : C → C with a Taylor series ∑ ∞ n=1 xn/an such the an’s form a “very fast growing” sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H .
منابع مشابه
Numerical solution of the Sturm-Liouville problem by using Chebyshev cardinal functions
In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem ...
متن کاملOn Generalization of Sturm-Liouville Theory for Fractional Bessel Operator
In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...
متن کاملSturm-Liouville Fuzzy Problem with Fuzzy Eigenvalue Parameter
This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.
متن کاملCanonical Quantization of the Liouville Theory , Quantum Group Structures , and Correlation Functions
We describe a self-consistent canonical quantization of Liouville theory in terms of canonical free fields. In order to keep the non-linear Liouville dynamics, we use the solution of the Liouville equation as a canonical transformation. This also defines a Liouville vertex operator. We show, in particular, that a canonical quantized conformal and local quantum Liouville theory has a quantum gro...
متن کاملNew inequalities for a class of differentiable functions
In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.
متن کاملOn a class of systems of n Neumann two-point boundary value Sturm-Liouville type equations
Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Log.
دوره 68 شماره
صفحات -
تاریخ انتشار 2003