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Suresh Kumar Bhatia (born 1952) is an Indian-born chemical engineer and professor emeritus at the School of Chemical Engineering, University of Queensland. [1] He is known for his studies on porous media and catalytic and non-catalytic solid fluid reactions. [ 2 ]
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures.
Say (,) is equipped with its usual topology. Then the essential range of f is given by . = { >: < {: | | <}}. [7]: Definition 4.36 [8] [9]: cf. Exercise 6.11 In other words: The essential range of a complex-valued function is the set of all complex numbers z such that the inverse image of each ε-neighbourhood of z under f has positive measure.
Rajendra Bhatia founded the series Texts and Readings in Mathematics in 1992 [5] and the series Culture and History of Mathematics on the history of Indian mathematics.He has served on the editorial boards of several major international journals such as Linear Algebra and Its Applications, and the SIAM Journal on Matrix Analysis and Applications.
Nonsmooth analysis is a brach of mathematical analysis that concerns non-smooth functions like Lipschitz functions and has applications to optimization theory or control theory. Note this theory is generally different from distributional calculus , a calculus based on distributions.
In mathematics, the Heinz mean (named after E. Heinz [1]) of two non-negative real numbers A and B, was defined by Bhatia [2] as: (,) = +, with 0 ≤ x ≤ 1 / 2 . For different values of x, this Heinz mean interpolates between the arithmetic (x = 0) and geometric (x = 1/2) means such that for 0 < x < 1 / 2 :
In mathematics, in particular functional analysis, the singular values of a compact operator: acting between Hilbert spaces and , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator (where denotes the adjoint of ).
The spectrum of a linear operator that operates on a Banach space is a fundamental concept of functional analysis. The spectrum consists of all scalars λ {\displaystyle \lambda } such that the operator T − λ {\displaystyle T-\lambda } does not have a bounded inverse on X {\displaystyle X} .