scholarly journals Wiener’s Theorem for Periodic at Infinity Functions

2012 ◽  
Vol 12 (4) ◽  
pp. 34-41 ◽  
Author(s):  
Irina Igorevna Strukova ◽  
Keyword(s):  
Wiener’S Theorem

An analog of Wiener’s theorem for infinite-dimensional Banach spaces

2015 ◽  
Vol 97 (1-2) ◽  
pp. 179-189
Author(s):  
A. V. Zagorodnyuk ◽  
M. A. Mitrofanov
Keyword(s):  
Banach Spaces ◽  
Infinite Dimensional ◽  
Wiener’S Theorem

scholarly journals Local Wiener’s theorem and coherent sets of frequencies

2020 ◽  
Vol 46 (4) ◽  
pp. 737-746
Author(s):  
S. Yu. Favorov
Keyword(s):  
Wiener’S Theorem

On the One-Sided Wiener's Theorem for the Motion Group

1980 ◽  
Vol 111 (3) ◽  
pp. 415 ◽  
Author(s):  
Yitzhak Weit
Keyword(s):  
Motion Group ◽  
Wiener’S Theorem ◽  
The One

17.—Absolutely Convergent Sturm-Liouville Expansions

1975 ◽  
Vol 73 ◽  
pp. 255-269
Author(s):  
S. D. Wray
Keyword(s):  
Fourier Series ◽  
Banach Algebra ◽  
Full Range ◽  
Second Order ◽  
Algebra Structure ◽  
Convergent Fourier Series ◽  
Wiener’S Theorem ◽  
Asymptotic Formulae ◽  
Sturm Liouville

SynopsisAn analogue of full-range Fourier series is introduced in the Sturm-Liouville setting and a theorem generalising Wiener's theorem for functions with absolutely convergent Fourier series is proved. The Banach algebra structure of the theory is examined. Use is made of second-order asymptotic formulae for the Sturm-Liouville eigenfunctions.

scholarly journals Analysis of the RSA-cryptosystem in abstract number rings

2020 ◽  
pp. 13-21
Author(s):  
Nikita V. Kondratyonok
Keyword(s):  
Quantum Computing ◽  
Quantum Computers ◽  
Rsa Cryptosystem ◽  
Factorization Problem ◽  
Wiener’S Theorem ◽  
Factorization Algorithms ◽  
Encryption Method

Quantum computers can be a real threat to some modern cryptosystems (such as the RSA-cryptosystem). The analogue of the RSA-cryptosystem in abstract number rings is not affected by this threat, as there are currently no factorization algorithms using quantum computing for ideals. In this paper considered an analogue of RSA-cryptosystem in abstract number rings. Proved the analogues of theorems related to its cryptographic strength. In particular, an analogue of Wiener’s theorem on the small secret exponent is proved. The analogue of the re-encryption method is studied. On its basis the necessary restrictions on the parameters of the cryptosystem are obtained. It is also shown that in numerical Dedekind rings the factorization problem is polynomial equivalent to factorization in integers.

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