Ground State for the Schrödinger Operator with the Weighted Hardy Potential

Ground State for the Schrödinger Operator with the Weighted Hardy Potential

Weighted Weak Type Inequalities for the Hardy Operator When

The paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted L to weighted weak L in the case p = 1. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when p = 1. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when q < p = 1. The best consta...

Weighted Inequalities for the Sawyer Two-dimensional Hardy Operator and Its Limiting Geometric Mean Operator

We consider T f = ∫ x1 0 ∫ x2 0 f (t1, t2)dt1dt2 and a corresponding geometric mean operator G f = exp(1/x1x2) ∫ x1 0 ∫ x2 0 log f (t1, t2)dt1dt2. E. T. Sawyer showed that the Hardy-type inequality ‖T f ‖Lq u ≤ C‖ f ‖Lp v could be characterized by three independent conditions on the weights. We give a simple proof of the fact that if the weight v is of product type, then in fact only one condit...

2 00 8 Hardy inequalities for weighted Dirac operator

An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight r for functions in R. The exact Hardy constant cb = cb(n) is found and generalized minimizers are given. The constant cb vanishes on a countable set of b, which extends the known case n = 2, b = 0 which corresponds to the trivial Hardy inequality in R. Analogous inequalities are proved in the ca...

Empirical Potential Energy Curve for the Ground State of CaH from a Multi-isotopologue Direct Potential Fit Analysis

Vibration-rotation and pure rotational data in the X2Σ+ ground state and electronic data from the A2Π – X2Σ+ and B2Σ+ − X2Σ+ transitions of CaH and CaD were used in the quantum-mechanical direct-potential-fit (DPF) analysis to determine an analytic potential energy function for the X2Σ+ ground state of CaH, and a radial correction function for the CaD isotopologue. The potential energy function...