A decreasing sequence of subharmonic functions is a sequence of functions where each function is subharmonic, meaning the Laplacian of the function is non-negative, and the functions decrease as the sequence progresses.
Studying decreasing sequences of subharmonic functions is important in the field of partial differential equations, as it can help in understanding the behavior and properties of solutions to certain types of equations.
A function is subharmonic if its Laplacian is non-negative, meaning the sum of its second-order partial derivatives is always greater than or equal to 0. This can be checked by calculating the Hessian matrix of the function and checking its eigenvalues.
Yes, decreasing sequences of subharmonic functions have applications in various fields such as physics, engineering, and economics. For example, in physics, they can be used to model heat flow and diffusion processes.
Some properties of decreasing sequences of subharmonic functions include monotonicity, meaning the functions either decrease or remain constant as the sequence progresses, and convergence, meaning the sequence of functions converges to a limit function as the number of functions in the sequence increases.