$$T(n) = 2\cdot \sqrt{n} \cdot T(\sqrt{n}) + \Theta (\lg n)$$I have been trying to solve this question but I could not find anything.My approach:$n = 2^k$  $S(k) = T(2^n)$ and $S(k/2) = T(2^{n/2})$Finally:$S(k) = 2^{1+k/2} \cdot S(k/2) + c \cdot \lg(k)  $After that, I tried to build recursion tree but I can not find the sum. Do you have any ideas?Thanks in advance.
Recursive Algorithm Analysis
recurrence relation