On the integrability of functions defined by trigonometrical series

1956 ◽  
Vol 66 (1) ◽  
pp. 9-12 ◽  
Author(s):  
Chen Yung-Ming
Keyword(s):  
Trigonometrical Series ◽  
Integrability Of Functions

On Trigonometrical Series with Mixed Conditions

1938 ◽  
Vol s2-43 (1) ◽  
pp. 366-375 ◽  
Author(s):  
W. M. Shepherd
Keyword(s):  
Trigonometrical Series

scholarly journals Some trigonometrical series, VIII

1954 ◽  
Vol 5 (3) ◽  
pp. 296-301 ◽  
Author(s):  
Shin-ichi Izumi
Keyword(s):  
Trigonometrical Series

scholarly journals Do Average Hamiltonians Exist?

1999 ◽  
Vol 172 ◽  
pp. 243-248
Author(s):  
S. Ferraz-Mello
Keyword(s):  
General Solution ◽  
Canonical Transformation ◽  
Trigonometrical Series ◽  
Averaging Methods ◽  
The Sixties

AbstractThe word “average” and its variations became popular in the sixties and implicitly carried the idea that “averaging” methods lead to “average” Hamiltonians. However, given the Hamiltonian H = H0(J) + ϵR(θ,J),(ϵ ≪ 1), the problem of transforming it into a new Hamiltonian H* (J*) (dependent only on the new actions J*), through a canonical transformation given by zero-average trigonometrical series has no general solution at orders higher than the first.

scholarly journals Some trigonometrical series, XIII

1955 ◽  
Vol 31 (5) ◽  
pp. 257-260
Author(s):  
Shin-ichi Izumi
Keyword(s):  
Trigonometrical Series

24.—Mean-square Convergence of Non-harmonic Trigonometrical Series

1976 ◽  
Vol 75 (4) ◽  
pp. 297-323
Author(s):  
J. Cossar
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Mean Square ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Real Numbers ◽  
Trigonometrical Series ◽  
Fixed Positive Number ◽  
Mean Square Convergence ◽  
The Difference

SynopsisThe series considered are of the form , where Σ | cn |2 is convergent and the real numbers λn (the exponents) are distinct. It is known that if the exponents are integers, the series is the Fourier series of a periodic function of locally integrable square (the Riesz-Fischer theorem); and more generally that if the exponents are not necessarily integers but are such that the difference between any pair exceeds a fixed positive number, the series is the Fourier series of a function of the Stepanov class, S2, of almost periodic functions.We consider in this paper cases where the exponents are subject to less stringent conditions (depending on the coefficients cn). Some of the theorems included here are known but had been proved by other methods. A fuller account of the contents of the paper is given in Sections 1-5.

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