منابع مشابه
A Lower Bound on the Cesaro Operator
If the sequence a = (a„>^ E /2, i.e., ||a||2 = 2~=0 | a„ |2 < oo, define Sa as the sequence of averages 1 " 2 ak n + 1 , It follows easily from the Marcinkiewicz Interpolation Theorem that S is a bounded operator from I2 to I2; this can also be proved directly using the Cauchy-Buniakowski-Schwarz inequality [1]. S is known as the Cesàro operator. S is, of course, not bounded below, but the foll...
متن کاملA Lower Bound for the Ground State Energy of a Schrödinger Operator on a Loop
Consider a one-dimensional quantum mechanical particle described by the Schrödinger equation on a closed curve of length 2π. Assume that the potential is given by the square of the curve’s curvature. We show that in this case the energy of the particle cannot be lower than 0.6085. We also prove that it is not lower than 1 (the conjectured optimal lower bound) for a certain class of closed curve...
متن کاملA universal lower bound for the first eigenvalue of the Dirac operator on quaternionic Kähler manifolds
A universal lower bound for the first positive eigenvalue of the Dirac operator on a compact quaternionic Kähler manifold M of positive scalar curvature is calculated. It is shown that it is equal to the first positive eigenvalue on the quaternionic projective space. For this, the horizontal tangent bundle on the canonical SO(3)-bundle over M is equipped with a hyperkählerian structure and the ...
متن کاملA lower bound on IMMSE �
This paper provides upper and lower bounds on the information rates achievable with a minimum mean square error (MMSE) Tomlinson-Harashima precoder (THP) assuming ideal interleaving. We also give an exact formula for zero-forcing (ZF) THP achievable information rates. At high SNR, the performance of the MMSE-THP and the ZF-THP identically suuer only the 2.55 bit or 1.53 dB \shaping" loss from c...
متن کاملA Lower Bound on the Transposition Diameter
Sorting permutations by transpositions is an important and difficult problem in genome rearrangements. The transposition diameter TD(n) is the maximum transposition distance among all pairs of permutations in Sn. It was previously conjectured [H. Eriksson et al., Discrete Math., 241 (2001), pp. 289–300] that TD(n) ≤ n+1 2 . This conjecture was disproved by Elias and Hartman [IEEE/ACM Trans. Com...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1982
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1982-0674108-9