The Bergman kernel function

Abstract

In this note, we point out that a large family of n×n matrix valued kernel functions defined on the unit disc D ⊆ C, which were constructed recently in [9], behave like the familiar Bergman kernel function on D in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered using this likeness.

Correlation of plastic deformation induced intermittent electromagnetic radiation characteristics with mechanical properties of Cu–Ni alloys

“…From Eqs. (8)(9)(10), can be evaluated in terms of and the mechanical/physical parameters of the material.Now starting with the first EMRs ignal at known valueo fn ear the yielding, each successive can be calculated and hencet he total numberofEMR emissions within the strain-hardening zone can be obtained.…”

Lα X-ray satellites for 31 ≤ Z ≤ 38: Systematization

“…A scrutiny of the compilation by Cauchois and Senemaud (1978) [6] reveals that in this atomic number range Lα 5 , Lα 6 and Lα 7 x-ray satellites are not available for the atomic numbers Z = 31 to 35, whereas the wavelengths for the Lα 3 and Lα 4 satellites are reported for the entire range Z = 31 to 38. All earlier theoretical attempts (1980-2012) [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] to calculate the energy values of the L -satellites cover only Z ≥ 39 and no calculations and interpretations have been made so far for the atomic number range Z= 31 to 38. Therefore efforts aiming to explain the origin of these satellites for Z = 31 to 38 becomes very important but can not be performed until the energy values for all the satellites and for the complete atomic number range Z= 31 to 38 become available.…”

Studies on crystals of d-, l-, and dl-alaninato nickel(II) complexes

“…The synthesis, spectrochemical properties, structure, stability, thermochemical study, and characterization of complexes of copper(II), nickel(II), cobalt(II), and zinc(II) with histidine, glycine, alanine, and other amino acids have previously been reported [8][9][10][11][12][13][14]. Standard molar enthalpies of formation of glycine and alanine in the gaseous phase on the basis of theoretical calculations have recently been studied [15].…”