Filtering for UI developed using GWT

I am developing an application using GWT as the front end technology stack. Backend stack is Struts, Spring, mybatis

We have a requirement to support column level filtering. for instance, if the client enters 'am', all words containing 'am' are filtering in the column. For GWT, to support filtering, what is the recommended approach: do we do the filtering in the front end using GWT or we develop the filtering logic in the backend and everytime the user tries to filter in the front end, we make a call to the backeng logic. Please explain pros and cons as this is a major functionality that cascades all screens.

Regards