Lower bounds for the Dyadic Hilbert transform

Some lower bounds for the $L$-intersection number of graphs

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

Some Lower Bounds for Estrada Index

Hilbert Transform and Gain/Phase Error Bounds for Rational Functions

It is well known that a function analytic in the right half plane can be constructed from its real part alone, or (modulo an additive constant) from its imaginary part alone via the Hilbert transform. It is also known that a stable minimum phase transfer function can be reconstructed from its gain alone, or (modulo a multiplicative constant) from its phase alone, via the Bode gain/phase relatio...

Upper and lower bounds for numerical radii of block shifts

For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...

New Uniform Bounds for a Walsh Model of the Bilinear Hilbert Transform

Abstract. We prove old and new L bounds for the quartile operator, a Walsh model of the bilinear Hilbert transform, uniformly in the parameter that models degeneration of the bilinear Hilbert transform. We obtain the full range of exponents that can be expected from known bounds in the degenerate and non-degenerate cases. For the new estimates with exponents p close to 1 the argument relies on ...