Recent content by Crot

Thank you for your answer. But, this concept is really too general. Are there any other techniques?

Could you please give me a hint on how to show that a set of operators with a property P is closed under addition? In other words, how one could prove that a sum of any two operators from the set still possesses this property P. The set is assumed to be infinite. Any references, comments...

Thank you for the answer! But, it is not what I meant. I did not mean the notation but the symbol of a differential operator which can be expressed as a polynomial. You know, when one works with pseudo-differential operators, for example, such kind of symbols appear in quantity. But, I heard...

Could someone please give a definition what the symbol of an integral operator is? Does it have asymptotic expansions as symbols of differential operators? I know about symbols of differential operators but, shame on me, heard nothing about the symbol of an integral operator. Any help in...

Thanks a lot for the answer. Now, it is clear!

Dear forumers, There is a wave computed in a 2D domain. Could you please give me a hint how to find the wavevector of the wave? I think I have to Fourier transform the wave in space but I cannot figure out how to obtain that k_x and k_y from the transformation. Crot

Thanks a lot to everyone who helped! I think I fathomed it out!

Thanks a lot for the detailed answer! It seems I found the gap in my understanding. Well, a tangent vector to f(x,y) lives on the tangent plane z=fx(x-x0)+fy(y-y0)+f(x0,y0) and it is perpendicular to the gradient of F(x,y,z) but, of course, the gradient of F(x,y,z) is not the gradient of...

Could you please give me an example of a tangent vector which is not perpendicular to the gradient at a given point?

Dear all, How could one find a tangential derivative of a function z=f(x,y) at a give point (x0,y0)? Is it always zero? I tried to go through in the following way. Well, if I need a tangential derivative f_t of a function f(x,y) I have to use a directional derivative in tangent direction...